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SWOOPE'S 

LESSONS IN 

PRACTICAL ELECTEICITY 

AN ELEMENTARY TEXT BOOK 



SIXTEENTH EDITION j 

REWRITTEN, REVISED: AND ENLARGED | 

i 

HARRY NOYES STILLMAN j 

LATE INSTRUCTOR AT THE SPRING GARDEN INSTITUTE, PHILADELPHIA 

AND i 

ERICH HAUSMANN, E.E., Sc.D. 

PROFESSOR OF PHYSICS AT THE POLYTECHNIC INSTITUTE OF BROOKLYN 

AND FELLOW OF THE AMERICA;^ INSTITUTE OF 

ELECTRICAL ENGINEERS 



488 ILLUSTRATIONS 



First Printing — Five Thousand 
Previous Issues — Sixty-eight Thousand 



NEW YORK 
D. VAN NOSTRAND COMPANY 
Eight Warren Street 
. 1920 






COPYRIGHT, 19OI, BY C. WALTON SWOOPE 



COPYRIGHT, 1908, BY O. L. SWOOPE 



COPYRIGHT, 1913, BY R. M. SWOOPE 



COPYRIGHT, 1920, BY 
D. VAN NOSTRAND COMPANY 



OCT 30 1920 
§)CI,A601288 



PREFACE 

The original edition of this book was written by Mr. C. 
Walton Swoope in 1900 primarily for the use of the evening 
classes in practical electricity at the Spring Garden Institute 
of Philadelphia. These classes were composed of young 
men engaged in various occupations who desired to obtain 
a working knowledge of the principles and arithmetic of ap- 
plied electricity. It was deemed best to divide the instruction 
between the lecture room and the laboratory, and accordingly 
the book was prepared to combine the principles of electricity, 
the experimental demonstration of these principles, and the 
methods used in practical electrical measurements and calcula- 
tions, with completely solved illustrations. The educational 
success attained at the Institute and at many other schools 
using this book has shown how well the author has solved the 
difficult problem of teaching electricity to the beginner. 

The book is also particularly adapted for self-study to those 
who desire electrical education; this has been amply demon= 
strated by its tremendous sale to individuals. 

Since the author's death in October, 1901, the book has been 
occasionally revised and enlarged by his former student, as- 
sistant and successor at the Spring Garden Institute, the fate 
Harry Noyes Stillman. Many men who to-day rank high 
in their professions owe their start and much of their success 
to the inspiring instruction and friendly advice of Mr. Stillman. 

The present enlarged and completely rewritten edition was 
commenced in 1918 by Mr. Stillman and myself, and was 
nearly completed at the time of his death in May, 1920. Some 
of the lessons have been merged and others strengthened, and 
all have been revised in keeping with the great advances made 
in electrical engineering. Three new lessons have been added, 
namely: Alternating-current Apparatus and Machinery, Al- 



iv PREFACE 

ternating-current Motors, and Radio Signaling. The last- 
mentioned lesson was prepared by Mr. Charles R. Underhill, 
recently Captain in the U. S. Air Service, who acknowledges 
his indebtedness for the data on Direction Finding to Mr, 
Herbert B. Basse tt. Thanks are extended to the various 
manufacturing companies of electrical apparatus for supplying 
the cuts of the devices and apparatus herein illustrated. 

E. Hausmann. 

Polytechnic Institute of Brooklyn, 
August 1, 1920. 



CONTENTS 

Lesson I 

MAGNETS 

Magnets — The Poles — Magnetic Attraction and Repulsion — 
Magnetic Substances — Making Permanent Steel Magnets — 
Magnetization — Laminated Magnets — Horseshoe Magnets — 
Practical Application of Permanent Magnets — The Earth as a 
Magnet — The Earth's Magnetism Used in Navigation — The 
Mariner's Compass — • Questions 1 

Lesson II 

MAGNETISM 

The Nature of Magnetism — Proof of the Molecular Theory of Mag- 
netism — • Magnetic Saturation • — The Magnetic Difference be- 
tween Iron and Steel — Magnetic Force — The Magnetic Field 
— ■ Axis and Equator of Bar Magnet — Magnetic Bodies Free 
to Move — ■ Magnetic Induction — Magnetic Screens — Conse- 
quent Poles — • Pole Pieces and Armatures — Questions 15 

Lesson III 

VOLTAIC ELECTRICITY 

Electricity — Electrical Effects — ■ Generation of Electric Currents 
by Chemical Means — A Current of Electricity — Simple Vol- 
taic Cell — • The Circuit — Conductors and Insulators — Direc- 
tion of the Current — Poles and Electrodes of a Cell — Detector 
Galvanometer — Potential and Electromotive Force — Chemical 
Action in a Voltaic Cell — Why the Hydrogen Appears at the 
Copper Plate — Polarization — Table I — On what the Electro- 
motive Force of a Cell Depends — The Electrochemical Series 
— Table II — Local Action — Amalgamation — ■ Questions .... 25 

Lesson IV 

PRIMARY CELLS 

Primary Cells ■ — • Open-Circuit Cells ■ — ■ Closed-Circuit Cells — Reme- 
dies for Polarization— The E. M. F. of Cells — Smee Cell — 



vi CONTENTS . \ 

Bichromate Cell — Fuller Bichromate Cell — Partz Acid Gravity J 
Cell — Bunsen and Grove Cells — ■ Daniell Cell — Leclanche 
Cell — Gonda Leclanche Cell — Carbon Cylinder Cell — Edison- 1 
I.alande Cell — Weston Standard Cell — Dry Cells — Classi- 
fication of Primary Cells — Chemicals for Cells and Some Chem- : 
ical Symbols — ■ Questions 40 ■ 

i 

Lesson V • ^ 

RESISTANCE j 

Resistance — The Unit of Resistance — Conductors and Insulators • 

— Table III — Wire Measure — The Circular Mil — The 1 
Square Mil — Laws of Resistance — Calculation of Resistance — • 
Table IV — Wire Calculations — Specific Resistance, Relative ! 
Resistance and Conductivity of Metals — Table V — The Wire 

Gage — Table VI — Internal Resistance of a Battery — Rheo- 
stats — Resistance of Connections — Laboratory Rheostats — " 

Questions and Problems 54 _; 

\ 
Lesson VI 

EFFECTS PRODUCED BY THE ELECTRIC CURRENT j 

Effects of the Current — Heating Effect — Magnstic Effect — ; 

Chemical Effect — Electrolysis — Electrolysis of Copper Sul- j 
phate — Electrolysis of Zinc Sulphate — Electrolysis of Lead 
Acetate — Electroplating — Electrotyping — ■ Polarity Indicator 

— Questions ^ 72 i 

Lesson VII | 

MEASUREMENT OF CURRENT j 

i 

Strength of Current — • Variation of Current and of the Current's Ef- • 

fects — How the Effects Vary with the Current Strength — j 

Variation of Effects with the Same Current Strength through j 
Dissimilar Apparatus — • Measurement of Current Strength — 

Definition of the Unit of Current Strength — Definition of a Unit , ) 

Quantity of Electricity — The Ampere-Hour — Weight Vol- ' 

tameters' — Voltameter Calculations — Construction of the Gas : 

Voltameter — Directions for Using the Gas Voltameter — \ 

Measuring Current Strength by a Gas Voltameter — Current • \ 

Strength Used in Electroplating — Table VII — Questions and ' 

Problems 80 



CONTENTS vii j 

Lesson VIII I 

OHM'S LAW ; 

Electromotive Force (Pressure) — Electromotive Force of Batteries 

— Table VIII — Ohm's Law — Circuits and their Resistance — i 
Resistances in Series — Equal Resistances in Parallel (Joint Re- 
sistance) — Conductance of a Circuit — Unequal Resistances in '; 
Parallel — Conductance Method for Conductors in Parallel — j 
Resistances Joined in Multiple-series — Division of Current in 

a Divided Circuit — Ohm's Law AppHed to a Battery Circuit — 
Questions and Problems 97 

Lesson IX 
SERIES AND PARALLEL BATTERY CONNECTIONS 

Methods of Varying Current Strength — The Size of a CeU — Cells 
Connected in Series to Increase the E. M. F. — Cells Con- 
nected in Parallel or Multiple for Quantity — The Internal Re- ■ 
sistance of Cells in Series — Current from Cells in Series — The 
Internal Resistance of Cells in Parallel or Multiple — Current 
from Cells in Parallel or Multiple — Advantage of Parallel Con- 
nection — Advantage of Series Connection — Cells Grouped in 
Multiple-series — Internal Resistance of Multiple-series Com- I 
bination of Cells — Current Strength from any Combination of 
Cells — Cells in Opposition — Questions and Problems 112 

Lesson X 

PRACTICAL APPLICATION OF OHM'S LAW 

I 

Electromotive Force and Potential Difference — Hydrauhc Analogy .j 

to Illustrate Volts Lost — Measurement of Electric Pressure — j 

Potential Difference, Current and Resistance of Parallel or Di- I 
vided Circuits — Volts Lost in an Electric Circuit — Distribution 

of Potential in a Circuit — Volts Drop in Wiring Leads — Varia- j 

tion of Potential Difference with Variation of External Resistance j 

— Table IX — Questions and Problems 128 ■ 

Lesson XI 
ELECTRICAL WORK AND POWER 

Force — Different Kinds of Force — Mass and Weight — Work — 
Power — Horse Power of a Steam Engine — Difference between 



viii CONTENTS 

Energy, Force, Work, and Power — Electrical Work — Electri- 
cal Power — Heat and Work — Equivalents of Mechanical and 
Electrical Work — Electrical Horse Power — The Kilowatt — 
The Watt-hour and Kilowatt-hour — Electrical Power Cal- 
culations — Power from Cells — EflBciency — Questions and 
Problems 144 



Lesson XII i 

STORAGE BATTERIES j 

The Storage or Secondary Cell — Direction of Current in a Storage ! 
Battery on Charge and Discharge — Chemical Action in a i 
Lead Storage Cell — ■ The Electrolyte in a Lead Cell — The \ 
Hydrometer — The Voltage of a Lead Storage Cell — Types of ; 
Lead Plates Used in Storage Cells — The Rated Capacity of a 
Storage Cell or Battery — ■ Care and Maintenance of Lead Cells j 
— 'The Nickel- Alkah or Edison »Storage Cell — -Efficiency of a ] 
Storage Cell — Methods of Charging — • Uses of Storage Bat- 
teries — Questions 161 i 

i 
] 

Lesson XIII j 

ELECTROMAGNETISM j 

Electromagnetism — Direction of Lines of Force around a Straight \ 

Current-carrying Wire — • Deflection of a Horizontal Magnetic \ 

Needle — 'Right-hand Rule for Direction of Magnetic Field j 

• around Wires — Magnetic Field around a Circular Wire Carrying ; 

a Current — Magnetic Field at the Center of a Circular Cur- i 

rent — Magnetic Polarity of a Circular Current — • The Hehx \ 

and Solenoid — • Rules for Determining Polarity of a Solenoid — ; 

Graphical Field of a Solenoid — ■■ Questions 185 i 

i 

Lesson XIV -] 

ELECTROMAGNETS I 

Magnetization of Iron and Steel by an Electric Current — Magnetic i 

Field of an Electromagnet — Attractive Force of a Solenoid i 

for an Iron Core — -Circuit Breakers — Magnetic Circuits — ! 

Typical Forms of Electromagnets, their Construction and Use — . i 

Polarized Electromagnets — Magnetomotive Force — Field In- I 
tensity — Law of the Magnetic Circuit — Magnetic Density, 



CONTENTS ix 

Permeability and Reluctance — Table X — Calculation of Mag- 
netic Circuits — Magnetization Curve — Attractive Force of an 
Electromagnet — Questions and Problems 196 

Lesson XV 
ELECTRODYNAMICS 

Reaction of a Current-carrying Wire on a Magnet — Automatic 
Twisting of a Current-carrying Wire aroimd a Magnetic Pole — 
Rotation of a Current-carrying Wire around a Magnetic Pole 

— Electrodynamics — The Magnetic Fields of Parallel Cur- 
rents — Laws of Parallel Currents — Currents in Conductors at 

an Angle with Each Other — • Questions 218 

Lesson XVI 
GALVANOMETERS 

Principle of the Galvanometer — ■ Detector Galvanometer — Sensi- 
bility of a Galvanometer — • Shunts — Tangent Galvanometer — 
Tables XI and XII — • Thomson Galvanometer — Reading De- 
vices for Mirror-type Galvanometers — Astatic and Differential 
Galvanometers -^^ D'Arsonval Galvanometer — The Ballistic 
Galvanometer — • Ayrton Shunt — Questions and Problems .... 228 

Lesson XVII 
AMMETERS AND VOLTMETERS 

Ammeters or Ampere-Meters — • Solenoidal Ammeter, Gravity Type 

— Thomson Inclined-Coil Ammeter — Weston A. C. Ammeters 

— Hot- Wire Ammeters — Weston D. C. Ammeters — Ammeter 
Shunts — Portable Dynamometer Ammeter; Electrodyna- 
mometer — Connecting Ammeters in Circuit — Measurement 
of E. M. F, and Potential Difference — Construction of Volt- 
meters — ■ Weston Direct-Current Voltmeters — Multipliers — 
Connecting Voltmeters — Potentionieter — Questions 247 

Lesson XVIII 
WATTMETERS AND WATT-HOUR METERS 

Measurement of Power and Energy — ■ Indicating Wattmeter — ■ 
Thomson Watt-Hour Meter — Sangamo Direct-Current Watt- 
Hour Meter — Reading the Watt-Hour Meter — Questions ... 268 



X CONTENTS I 

I 

Lesson XIX j 

MEASUREMENT OF RESISTANCE I 

Resistance Standards — Voltmeter and Ammeter Method of Measm*- ' 

ing Resistance — Substitution Method of Measuring Resistance ". 

— Comparative Drop Method of Measuring Resistance — Volt- ; 

meter Method of Measuring Resistance — Wheatstone Bridge 

Method of Measuring Resistance — The Slide- Wire Bridge — 

Commercial Wheatstone Bridges and Portable Testing Sets — 

Ohmmeters — ■ Questions and Problems 279 i 

Lesson XX 

ELECTRICAL DEVELOPMENT OF HEAT I 

Heating of Conductors and their Safe Current- Carrying Capacity — j 

Table XIII — Electrical Development of Heat — Electrical ! 

Equivalent of Heat — Relation between Heat, Mechanical and * 

Electrical Energy — Relation between Fahrenheit and Centi- ; 

grade Thermometer Scales — Dependence of Resistance upon : 

Temperature — • Table XIV — Fuses — Electric Welding — ■ 

Electric Cautery, Blasting, Heating and Cooking — Measure- | 

ment of Temperature by Resistance Change; , Pyrometry — j 

Thermo-electric Pyrometers — Table XV — Questions and , 

Problems 305 i 



Lesson XXI J 

ELECTROMAGNETIC INDUCTION ; 

Electromagnetic Induction — E. M. F. Induced in a Wire by a Mag- ; 
net — 'To Find the Direction of the Induced E. M. F. — Value 

of the Induced E. M F — t'Lenz's Law of Induced Currents- — j 

Currents Induced by Electromagnetism ■ — Table XVI — Varia- j 

tion of Induced E. M. F. with the Rate of Change of Magnetic \ 

Lines of Force — ■ Eddy Currents — • Magnetic Hysteresis — Mu- ] 

tual Induction — • Self-induction — Inductance — Reactance 1 
and Impedance — Neutralizing the Effects of Self-induction — 

Questions 326 ! 

I 

Lesson XXII [ 
PRACTICAL APPLICATIONS OF ELECTROMAGNETIC 

INDUCTION — TELEPHONY ■ 

Practical Application of Induction — The Spark Coil — Principle of 

the Induction Coil — Action of the Condenser — Construction ; 

i 
1 



CONTENTS xi | 

of Induction Coils — Table XVII — Interrupters for Induction 
Coils — Induction Coils for Automobile Ignition Systems — | 

Vacuum Tubes — X-Rays — The Fluoroscopic Screen and j 

Fluoroscope — The Telephone — Telephone Systems — Tele- J 

phone Switchboards in Central Offices ■ — Questions 348 | 

i 

Lesson XXIII I 

PRINCIPLES OF DYNAMO-ELECTRIC MACHINES . : 

Dynamos — Classification of C^enerators — A Simple Generator — j 

Alternating-Current Generator — Graphic Representation of an : 

Alternating Current — Magneto Alternator — Simple Direct- • 

Current Generator — Graphic Representation of a Direct Cur- ■ 

rent — Multi-Coil Armatures — Principle of the Motor — | 

Direction of Rotation of Motors — Questions 372 : 

Lesson XXIV 

ARMATURES : 

Gramme Ring Armatm^e — Induced E. M. F. in a Ring Armature — | 

Drum Armature — Open-Coil Armatures — Eddy-Current Loss - 

— The Commutator and Brushes — Armature Core Insulation 

— Table XVIII — Armature Windings — Hysteresis Loss — i 
Armature Reactions — The Act of Commutation of an Armature 

Coil — Improvements in Commutation — Causes of Sparking — 

Questions 389 ■ 

Lesson XXV : 

DIRECT-CURRENT GENERATORS 

Classification of Dynamos according to their Field Excitation — The ; 

SeK-exciting Principle of Direct-Current Generators — Residual 
Volts — The Shunt Generator — Action of the Shunt Generator 

i 

— Action of the Series Generator — Compound Machines — ; 
Compound-wound Generators in Parallel — Three- Wire Genera- ^ 
tors — Capacity of a Generator — Commercial Rating of Gen- I 
erators — Losses in a D5mamo — Efficiency of a Generator — ! 
Questions and Problems 416 j 

Lesson XXVI 1 

DIRECT-CURRENT MOTORS 1 

Comparison between a Generator and a Motor — Direction of Rota- ] 

tion of Series and Shunt Motors — Position of the Brushes on a 



xii CONTENTS ! 

Motor — Counter Electromotive Force of a Motor — Current [ 
Taken by a Motor — Mechanical Power of a Motor — Torque 

— Output and Efficiency of Motors — Starting Motors — Speed ' 
Control of the Shunt Motor — Speed Regulation — Character- 
istic Curves of Motors — Electric Traction — Direct-Current ; 
Motor-Generator Sets — Questions and Problems 440 \ 

Lesson XXVII ! 

ELECTRIC LIGHTING ■ 

Arc Lamps — Flaming Arc Lamp — Special Forms of Arc Lamps — i 
Mercury Vapor Lamp — Incandescent Lamps — Lamp Fila- 
ments — Commercial Rating of Incandescent Lamps — Effi ■■ 
ciency and Life of a Lamp — Table XIX — Light Distribution 
Curves — Incandescent Lamp Circuits — Potential Distribution | 
in Multiple-Lamp Circuits — Loss on Line Wires — Incandescent ■ 
Wiring Calculations — The Three-Wire System — Motor Wiring J 
Calculations — Installation of Interior Wiring — Questions and 1 
Problems 464 

Lesson XXVIII 

ALTERNATING CURRENTS ' 

Principles of Alternating Currents — Theory of Alternating Currents ' 

— Sine Curves — Frequency, Alternations and Cycles — In- \ 
ductance — Reactance — Impedance — Graphical Illustrations | 
of Impedance, Reactance and Resistance — Capacity — Peculi- i 
arities due to Inductance and Capacity — Impedance of Circuits ' 
Having Inductance, Capacity and Resistance — Ohm's Law for ■ 
Alternating-Current Circuits — Impedances in Series — Im- \ 
pedances in Parallel — Effective Values of Alternating Currents ! 
and E. M. F.'s. — Components of Impressed E. M. F. — ' 
Angle of Lag or Lead, and Phase — Determination of Power 
Expended in Alternating-Ciu-rent Circuits — Questions and j 
Problems 494 I 

liESSON XXIX 

ALTERNATING-CURRENT APPARATUS AND MACHINERY 

.Transformers — Transformer Regulation and Efficiency — Transform- " | 

ers on Polyphase Circuits — Alternators — Revolving- Armature i 

. Alternators — Revolving-Field Alternators — Inductor Alter- i 



CONTENTS xiii : 

nators — Power Rating of Alternators — Conversion — Rotary -j 

Converters — Rectifiers — Questions and Problems 527 

Lesson XXX ; 

ALTERNATING-CURRENT MOTORS 

Polyphase Induction Motors — Squirrel-Cage and Wound Rotor 

Induction Motors — • Starting of Polyphase Induction Motors i 

and Speed Control — ■ Single-Phase Induction Motors — Single- - | 

Phase Commutator Motors — • Synchronous Motors — Starting ^ 

of Synchronous Motors — Motor-Generator Sets — Questions 554 j 

i 
Lesson XXXI 

RADIO SIGNALING 

Electromagnetic Waves — Table XX — The Production of Electro- 
magnetic Waves — Frequency, Oscillation Constant and 

Wave Length — Damped Waves and Continuous Waves — j 
Types of Antennas — Methods of Exciting the Antenna Circuit 

— Table XXI — Continuous-Wave Transmission Systems — ^ 
Radio Frequency and Audio Frequency — Radio Receiving Sets • 
— ■ Vacuum Tubes — The Vacuum Tube as a Detector and an ' 
Amplifier — The Vacuum Tube as an Oscillation-Generator or j 
Oscillator — How the Waves Leave the Transmitting Antenna i 

— Loop Reception — Radio Direction Finder — Questions .... 579 j 

i 
Appendix 611 | 

I 
Index 615 1 



LESSONS IN 
PRACTICAL ELECTRICITY 



LESSON I 

MAGNETS 

Magnets — The Poles — Magnetic Attraction and Repulsion — Mag- 
netic Substances — Making Permanent Steel Magnets — Magneti- 
zation — Laminated Magnets — Horseshoe Magnets — Practical 
Application of Permanent Magnets — The Earth as a Magnet — The 
Earth's Magnetism Used in Navigation — The Mariner's Com- 
pass — Questions. 

1. Magnets. — The name magnet was first applied by the 
ancients to lead-colored stones, known as oxide of iron, mag- 
netite, Fe304, because they possessed the power of attracting 
small particles of iron or steel. Later, the Chinese discovered 
that if a piece of the ore was freely suspended, it would assume 
a position pointing north and south; hence, they gave it the 
name of lodestone (meaning leading stone). 

If the lodestone is dipped into iron filings, it will be found 
that the attraction for the filings seems to be centered at two 
or more points on the stone, while at other points no filings are 
attracted. This property of attracting iron and steel is called 
magnetism, and a body possessing it is called a magnet. The 
lodestone is called a natural magnet, since it possesses magnet- 
ism when taken from the earth. 

The natural magnet possesses a third important property, 
namely, that of imparting all of its properties to a small piece 
of hard iron or steel when they are rubbed together. Besides 
the natural magnet, magnets are classified into artificial, per- 
manent, and temporary magnets. A piece of steel rubbed with 
lodestone, or magnetized in any other way, becomes an artificial 

1 



LESSONS IN PRACTICAL ELECTRICITY 




Fig. 1. — Natural Magnet 
Attracting Iron Filings. 




magnet, and if the steel retains its magnetism indefinitely, it 
would be termed a 'permanent magnet. A temporary magnet is 
any magnetizable substance that possesses the property of at- 
tracting filings while under the influ- 
ence of another magnet. Figs. 1 and 
2 illustrate a natural and an artificial 
magnet respectively. A magnet would 
he defined as a piece of steel, or other 
magnetized substance, which possesses 
the properties of attracting other pieces 
of steel or iron, or magnetizable bodies to it, and of pointing, when 
freely suspended in a horizontal position, toward the north pole of 
the earth. 

2. The Poles. — In observing Fig. 2 it will be noted that 
the attraction of the magnet for the filings is greatest at both 
ends of the magnet, and 
that there is practically no 
attraction at the center. 
The ends of a magnet, 
where the attraction is 
strongest, are termed its 
poles. The end which points 
toward the north geographical pole is generally called the North 
pole, and is usually marked on that end of 
the magnet by an N, or a line cut in the 
steel, while the other, unmarked, end is the 
South pole. By the term polarity we mean 
the nature of the magnetism at a particular 
point ; that is, whether it is north- or south- 
seeking magnetism. 

3. Magnetic Attraction and Repulsion. — 
If a thin piece of magnetized steel in the 
form of an elongated lozenge be pivoted so 
that it is free to move, it will assume a 

Pig 3 Horizontal definite direction pointing north and south. 

Magnetic Needle. When a magnet is thus mounted, it is 

termed a horizontal magnetic needle (Fig. 3) . 

A small magnetic needle, poised on a jewel bearing above a 

graduated scale, fastened to, or engraved on a containing box, 



Fig. 2. 



Magnetized Steel Bar Attract- 
ing Iron Filings. 





MAGNETS 




having a glass cover, is termed a compass (Fig. 4). Either 
the compass or horizontal needle may be used for determining 
the polarity of magnets and for 
studying magnetic attraction 
and repulsion. 

Experiment 1. — With the mag- 
netic needle or compass referred to 
above, and a bar magnet held in the 
hand, bring the N-pole of the magnet 
to the N-pole of the needle (Fig. 5) ; 
repulsion of the N-end of the magnetic 
needle occurs. The same effect will 
be noted if two South poles are brought 
near each other. If, however, the S- 
pole of the magnet is brought near 
the N-pole of the needle (Fig. 6), at- 
traction of the magnetic needle occurs. 

Like poles repel each other, Fig. 4. — Magnetic Compass. 
and unlike poles attract each other. 

The above experiment can be made 
with a piece of lodestone and the loca- 
tion and polarity of the several poles in 
the lodestone determined. 

4. Magnetic Substances. — There is a 
distinction between magnets and mag- 
netic substances. A magnet attracts 
only at its poles. A piece of iron will 
attract a magn'et, no matter what part 
of it approaches the magnet ; it does not 
possess fixed poles or a neutral point, 

while a magnet has at least two poles, N^ 

one of which always repels one pole of 
another magnet. 

The magnetic metals used in practice 
are steel and iron. Besides these, the 
metals nickel, cobalt, chromium, and 
cerium are attracted by a magnet, but 
only very feebly. Nickel and cobalt are 
the best of this class, but are very in- 
ferior to iron or steel. For practical purposes all other sub- 
stances, such as copper, lead, gold, platinum, wood, rubber, 




Fig. 5. — N-Pole Repels 
Another N-Pole. 




Fig. 6. — S-Pole At- 
tracts a N-Pole. 



LESSONS IN PRACTICAL ELECTRICITY 



glass, etc., may be regarded as unmagnetizable, or nonmagnetic 
substances. Magnetic attraction or repulsion will, however, 
take place through these substances. 

5. Making Permanent Steel Magnets. — Some varieties of 
steel which possess good machine-tool properties are not 
adapted to making good permanent magnets. Steel contain- 
ing a certain percentage of manganese cannot be magnetized, 
while some brands of cast steel, spring steel, and mild plate 
steel are readily magnetized, but do not retain their magnetism 
permanently. The best permanent magnets are made from a 
special brand of steel known as magnet steel. If the special 
magnet steel cannot be obtained, a piece of good, close-grained, 
rolled steel that has not been heated since it was made will do; 
the steel should be ''glass hard," that is, tempered by being 
heated to a red heat and suddenly immersed in water or oil. 
It will become very brittle and can be magnetized by any of 
the methods hereafter given. 

6. Magnetization. — A bar of steel, after being tempered, 
may be magnetized by either of the methods illustrated in 

Figs. 7 and 8, where use is made of 
another strong permanent magnet. 

The bar to be magnetized is laid on 
a table and, beginning at the unmarked 
end of the steel bar, stroke its entire 
length with the South end of the strong 
permanent magnet. Lift the magnet 
clear at the end and return again for 
a second stroke in the direction of the 
dotted line and arrows in Fig. 7. 
Stroke all sides of the bar you are mag- 
netizing about ten times in this manner. This is known as the 
single-stroke method. After magnetizing the bar of steel, it 
may be tested by suspending it, noting if the marked end points 
toward the north when it comes to rest. Note that the N-pole 
in the magnet you have made was always touched last by the 
S-pole of the magnetizing magnet. One pole always induces 
the opposite pole in any magnetizable body at the point where 
the pole last leaves that body, % 2L 

A stronger magnet will be obtained by magnetizing each 



-i 






umm 



Fig. 7. — Magnetizing 
a Steel Bar with a Per- 
manent Magnet (Single- 
stroke Method) . 



MAGNETS 



half separately, as illustrated in Fig. 8. Stroke one half of 
the steel bar with the S-pole, beginning at the center and 
following the direction of the dotted lines. Repeat this a 
number of times on each side; then, using the N-pole, stroke 
the other half in the same way. 

A still better method of magnetization is by means of an 
electric current. If a number of turns of insulated wire be 

In 



y 



^ 



m 



N' 



N' 



Fig. 8. — Magnetizing Each Half Separately. 



wrapped around the steel bar (Fig. 9) to be magnetized, and 
a strong current of electricity passed through the coil from a 
battery or an electric generator, the steel will be found per- 
manently magnetized with a N-pole and a S-pole after the 
current is turned off. Instead of winding the wire around the 
bar, the bar can be inserted in a spool containing many turns 
of insulated wire, through which the electric current is passed. 




Fig. 9. — Magnetization by an Electric Current. 

7. Laminated Magnets. — If a thick piece of steel be mag- 
netized and then placed in an acid bath (such as nitric acid) 
for some time, whereby the outer surface is eaten off, and then 
tested for magnetic qualities, it will be found to be almost 



6 



LESSONS IN PRACTICAL ELECTRICITY 




Fig. 10. — Laminated 
Horseshoe Magnet. 



/^-c-. 



entirely demagnetized. From this experiment it is inferred 
that the magnetism has only penetrated the surface of the 
steel. If a permanent magnet then be 
made up of a number of thin pieces of steel, 
magnetized separately, and fastened together 
with like poles at the same end, it will be 
stronger than one of solid steel of the same 
dimensions, because it is more thoroughly 
magnetized. Such magnets can be made in 
any form and are known as laminated mag- 
nets; a horseshoe laminated magnet is 
shown in Fig. 10. 

8. Horseshoe Magnets. — When a straight 
bar of steel is bent into the 
form of a horseshoe, and 
then properly magnetized; 
the end of one limb will be a N-pole and the 
other a S-pole. By bringing the poles close 
together in this manner the magnet will exert 
a force much greater than the sum of the 
attractive forces when used separately; be- 
cause in a bar magnet only one pole could 
be used at a time, while now both poles act 
together. A piece of soft iron, called the 
keeper, is placed across the ends of the poles 
when they are not in use, to assist in pre- 
venting the loss of magnetism. Fig. 11 illus- 
trates a horseshoe magnet of rectangular 
cross section, with its keeper, K, attached. Fig. 12 illustrates 

the proper method of 
putting away two 
bar magnets with 
their keepers, to pre- 
vent loss of mag- 
netism ; the unlike 
poles are placed at 
the same end, with the keeper connecting them. 

9. Practical Application of Permanent Magnets. — Per- 
manent magnets are used extensively in electrical measuring 



n\\\ 


1 


^feT-- 


f./n 


^K 




Fig. 11. — Horse- 
shoe Magnet and 
Keeper. 




Fig. 12. — Student's Magnet Set. 



MAGNETS 




the Weston Electrical 
Measuring Instru- 
ments. 



instruments. Fig. 13 illustrates a powerful horseshoe magnet 
used by the Weston Electrical Instrument Company for their 
portable ammeters and voltmeters for direct-current work. 
Fig. 14 illustrates the form of permanent magnet used to 
produce a load or drag on the copper disk 
in the Thomson watt-hour meter. 

Permanent magnets may also be found 
in nearly all telephone receivers and mag- 
neto-electric generators. It is quite impor- 
tant that magnets used for these purposes 
should not change appreciably in magnetic 
strength with time. In order that such 
magnets will not suffer any appreciable loss sho^'liagneU^erfn 
of their high magnetic strength when used, " ~' 

they are put through a process of aging. 
They are subjected to certain temperature 
changes and vibrations, which have the effect of settling 
their strength at a value that is nearly permanent. 
Permanent magnets, or instruments containing them, 

should be handled with great care, 

as heat and rough treatment will 
soon weaken them. 

10. The Earth as a Magnet. — 
Experiment 1 would indicate two 
kinds of magnetism, or two kinds 
of magnetic poles, which attract 
or repel each other, one pole tend- 
ing to move toward the geographical 
north pole, and the other pole toward the geographical south 
pole. Since we have called the north-pointing, or marked pole, 
the N-pole, then the magnetism of the earth near the north 
geographical pole must be of the opposite kind, or south mag- 
netism, since unlike poles attract each other. A compass needle 
assumes the position pointing north and south, because the 
earth possesses the property of a magnet, having a magnetic 
North and South pole. 

The true S magnetic pole is located in the northern hemi- 
sphere, while the true N magnetic pole is in the southern 
hemisphere (Fig. 15). The earth's true magnetic S-pole is 




Fig. 14. — Form of Horseshoe 
Magnet Used in the Thomson 
Watt-hour Meter. 



8 



LESSONS IN PRACTICAL ELECTRICITY 



^ North 
South ' i'^ .^Geographical Po/e 



not coincident with its north geographical pole, but about 1400 
miles away from it. A compass needle points its north-seeking 
pole in the direction of the S magnetic pole; this deviation of 
the needle's N-pole from the geographical north pole in general 
becomes more marked as the compass needle 'is carried farther 
north on the earth. This deviation of the needle is known as 
the angle of declination of any given place, and indicates just 

how far away from, the 
true geographical north 
the compass needle points. 
If a steel knitting needle 
be carefully balanced and 
suspended by a silk thread, 
it will assume a horizon- 
tal position. When it is 
magnetized, its N-end will 
point downward in the 
northern hemisphere or 
dip toward the earth's 
magnetic S-pole. This 
needle, being free to move 
in all directions, assumes 
a position pointing in the 
direction of the earth's 
magnetic force. The angle 
horizontal is termed the 




■ --^ / IMagncfic Pole 

y I ' 

Fig. 15. — The Earth's Magnetic Poles 
and Equator. 



which the needle makes with the 
angle of dip. The dip needle is horizontal at the magnetic 
equator, the angle of dip increasing as you go toward either 
magnetic pole. 

An imaginary line encircling the earth midway between its 
magnetic poles and connecting all those points which show no 
magnetic dip, or where the dip needle was found to be hori- 
zontal, is called the magnetic equator, just as the geographical 
equator is an imaginary belt passing around the earth midway 
between its poles (Fig. 15). The magnetic equator is some- 
what irregular in form, owing to the irregular distribution of 
the earth's magnetism. 

11. The Earth's Magnetism Used in Navigation. — In If 10 
the angle of dechnation at any given place is defined as the 



MAGNETS 



9 



deviation of the magnetic needle from the true north; it may 
also be defined as the angle between the magnetic meridian and 




o 


a 






03 








(/) 


a 
















(U 




73 
















S 






«4-( 


bfl 


O 


C 






c3 


> 

r, 


^ 


^ 


o 


03 












•o 


03 




^ 


^ 










1 


O 










CO 




T-H 


n 






hO 


H-( 






l^ 





the geographical meridian, since the magnetic meridian at a 
location is the direction of a magnetic needle at that location, 



10 LESSONS IN PRACTICAL ELECTRICITY 

as the line AB (Fig. 15). The magnetic meridian may be re- 
garded as an imaginary hne drawn on the earth in a plane which 
passes through the magnetic poles of the earth and a given 
place. The geographical meridian is an imaginary line drawn 
on the earth's surface in a plane which passes through the geo- 
graphical poles and a given place, as line AC (Fig. 15). The 
angle between lines AB and AC is known as the angle of dec- 
lination at point A. 

The angle of declination varies at different locations on the 
earth's surface and is slowly. but constantly changing. In 
Columbus, Ohio, and Charleston, South Carolina, in 1900, the 
declination was zero; that is, the geographic pole was just in line 
with the magnetic pole at these points, or the two meridians 
coincided. Moving west from point A (Fig. 15), the declina- 
tion decreases until a locality is found in Central Asia where 
the meridians again coincide. Places in the Atlantic Ocean, 
Europe, and Africa, between these lines of no declination, 
would have a declination west of the true north, while at 
places on the other side of the globe between these lines the 
needle would point east of the true north. 

In steering ships at sea by the compass, references are made 
to a chart, giving the values of the declination of the mag- 
netic needle at different localities on the earth's surface. The 
charts, or magnetic maps, are prepared by the United States 
Geodetic Survey and, in addition to giving the angle of decli- 
nation at different localities, it contains lines connecting places 
of equal magnetic declination, called isogonic lines (Fig. 16). 

12. The Mariner's Compass. — The small pocket compass 
(Fig. 4) is merely a nicely balanced and pivoted magnet, con- 
tained in a brass case to exclude disturbing draughts of air, and 
provided with a suitable scale indicating north, south, and inter- 
mediate points. In using this compass to determine direction, 
it is first necessary to permit the needle to come to rest so 
as to point north and south, and then gently twist the box 
around until the point marked N on the scale is directly under 
the N-pole of the needle. The true geographical north will 
then be so many degrees east or west of the position assumed 
by the N-pole of the needle on the scale, depending on the 
amount of declination. 



MAGNETS 



11 



The mariner^s magnetic compass, which is quite sensitive 
and arranged for nautical observations, may be either of the 
" dry-card " type or of the " hquid " type. In the dry-card type 
the magnetic needle is fastened to the under side of a card- 
board scale, which is pivoted inside the compass bowl. The 
scale is divided into the thirty-two '' points of the compass" 
(Fig. 17), and swings with the magnetic needle; the N-point 
on the scale always points to the north. When it is desired 
to steer in any particular direction, as northwest, the ship's 
helm is turned till the point' 
NW on the movable scale is 
opposite a fixed vertical black 
line (termed the " lubber's 
line "), which is drawn on the 
inside of the compass bowl, in 
line with the direction of the 
ship's motion. The compass 
box is supported on gimbal 
bearings, so that no matter how 
much the ship may roll or lurch 
the card will always be level. 

The magnetic compasses of 
the liquid type were first de- 
veloped in this country, and 
after many years of trial have been found to be better adapted 
for naval use than the dry-card compass, and are now gener- 
ally used throughout the world on naval vessels. The advan- 
tage of their use is the greater steadiness of the card when 
subjected to the shock of gun-fire and the greater steadiness 
in a rough sea. The liquid compass allows the use of more 
powerful magnets, and therefore has greater directive force and 
sensibility. 

The construction of a standard liquid compass used in the 
.Navy is shown in Fig. 18. In the center of the card P is 
located a spheroidal air-vessel Q to buoy the card and magnets, 
which are immersed in the liquid (45 per cent alcohol and 55 per 
cent distilled water) which entirely fills the bowl, D. The mag- 
nets O consist of four cylindrical bundles of highly magnetized 
steel wires contained in sealed cyhndrical cases, the magnets 




Fig. 17. — Scale of the Mariner's 
Compass. 



12 



LESSONS IN PRACTICAL ELECTRICITY 



being placed parallel to the north and south line of the card. 
The cast bronze bowl is weighted with lead J at the bottom. 
A pivot M is fastened to the bottom of the chamber, which 
supports and also keeps the card P in its position. Beneath 
the bowl is a self-adjusting expansion chamber K, of elastic 
metal, having two small holes, L, to permit circulation of the 
liquid between the bowl and expansion chamber, thus keeping 
the bowl free from bubbles. Two lubber's lines are drawn on 
enameled plates inside the bowl. The bowl is supported in 
gimbal bearings; B is one gimbal ring and A is one of its 
knife edges which rests on the other gimbal ring. The bowl 




Fig. 18. — Sectional View of the Liquid Type of Magnetic Compass. ' 

and compass card are accurately balanced with lead weights. ; 

The scale for this compass is the same as shown in Fig. 17. j 

Mariner's magnetic compasses require frequent adjusting in ■ 

order to insure accuracy, and many precautions have to be i 

taken in adjusting a ship's compass to compensate for errors ; 

likely to arise, due to the influence on the magnetic needle of \ 

the hull, of the cargo, or of electric light wires in the vicinity, ; 

etc. i 

A compass that is not dependent upon the earth's magnetic j 

force for the movement of the " card " is the " gyro-compass." ] 

Gyro-compasses are now being installed by the Navy De- i 

partment on all new battleships and submarines. The dif- ; 
ficulty in properly compensating magnetic compasses on such 

vessels, for various magnetic latitudes, has increased greatly ; 



MAGNETS M3 

with the increase in size of the vessels, and with the use of 
great masses of moving steel in the turrets and guns. The 
gyro-compass, being subject to no magnetic influence whatever, 
has solved the problem of obtaining an efficient battle compass, 
and experience has demonstrated that it is also to be used for 
navigation purposes practically at all times. The magnetic 
compass, however, will always be retained for a check on the 
gyro-compass, and for use in case of casualty to the latter. 
The advantages of the gyro-compass over the magnetic com- 
pass are: it is not subject to magnetic influence, or to sudden 
changes in magnetic condition, resulting from the training of 
turrets and boat cranes, operation of electric generators or 
motors, etc. ; it always points true north, thereby eliminating 
magnetic declination and its variations; it maintains a steady 
heading while rolling, and is sensitive only to actual changes 
in course. 

The operation of the gyro-compass is based on the principle 
of the gyroscope, which consists essentially of a heavy rotating 
wheel, the axis of which is free to turn in any direction. When 
the wheel is revolving at high speed its axis assumes a position 
parallel to the axis of the earth. For a description of the con- 
struction and operation of the gyro-compass, the student is re- 
ferred to " Practical Manual of the Compass," published by the 
Naval Institute, Annapohs, Maryland. 



QUESTIONS 

1. What is a natural magnet? 

2. What three important properties does it possess? 

3. How would you locate the poles on a natural magnet? 

4. Distinguish between a natural and an artificial magnet. 

5. You are given two similar bars of steel, only one of which is mag- 
netized. What tests would you apply to determine which one is mag- 
netized? 

- 6. Define a magnet. 

7. State the law regarding magnetic attractions and repulsions. 

8. What is the difference between a magnet and a magnetic substance? 

9. What do you mean by polarity? 

10. A bar magnet is floated on a cork; the N-end is toward the observer. 
What occurs when a S-pole is approached to the S-end of the floating 
magnet? What effect when the N-end is approached to this same end? 



14 LESSONS IN PRACTICAL ELECTRICITY 

11. What is the difference between a permanent and a temporary 
magnet? Give an example of each class. 

12. You are given a hard steel bar with a notch filed at one end. How 
would you magnetize it by using the N-pole of a magnet so that the notched 
end would have a N-pole? 

13. What two tests would you apply to prove that although a piece of 
iron attracts the N-pole of a suspended bar magnet yet it is not itself a 
magnet? 

---14. Give a general classification of magnets, citing an example to 
illustrate each class. 

15. How would you magnetize a steel sewing needle by the method 
of magnetizing each half separately, so that the eye would be a N-pole? 
Give a sketch. 

16. What kind of steel would you select to make a good permanent 
magnet? 

17. What is a laminated magnet? How would you put four horse- 
shoe magnets together to make a laminated magnet? 

18. What is the advantage of laminated magnets over those made 
from solid steel? 

19. Describe the liquid type of magnetic compass. 

20. What are isogonic hnes? 



LESSON II 



MAGNETISM 



The Nature of Magnetism — Proof of the Molecular Theory of Magnetism 
— Magnetic Saturation — The Magnetic Difference between Iron 
and Steel — Magnetic Force — The Magnetic Field — Axis and 
Equator of Bar Magnet — Magnetic Bodies Free to Move — Mag- 
netic Induction — Magnetic Screens — Consequent Poles — Pole 
Pieces and Armatures — Questions. 

13. The Nature of Magnetism. — The so-called molecular 
theory of magnetism is offered as an explanation of the phe- 





2^ 



n s 

■ Possible Arrangement of Molecular Magnets 
in Unmagnetized Bar (Magnified) . 

nomena arising from the magnetism of a piece of steel or iron. 
The theory assumes that a bar of steel or iron, composed like 
all matter of small molecules, is made up of minute magnets. 
If the steel or iron is not magnetized, these molecules arrange 
themselves promiscu- 
ously in the body; 
but according to the 
law of attraction and 
repulsion between un- 
like poles, the mag- 
netic circuits are satis- 
fied internally, and there is no resulting external magnetism. 
Fig. 19 illustrates several possible geometric figures which the 
molecules may assume in an unmagnetized bar of steel or 

15 




Fig. 20. 



Glass Tube of Steel Filings before 
Magnetization. 



16 



LESSONS IN PRACTICAL ELECTRICITY 



iron. When the bar is magnetized, the molecules rearrange 
themselves according to the law of attraction, turn on their 
axes, and assume positions more nearly in a straight line, with 
their N-ends pointing the same way. The closed magnetic cir- 
cuits are thus broken up, and external magnetism made evident. 
14. Proof of the Molecular Theory of Magnetism. — • 

Experiment 2. — Fill a small glass tube with coarse steel filings, and 
insert a cork at each end. Test each end of the tube for magnetism by 

bringing it near a sus- 



cirv" 




Glass Tube of Steel Filings after 
Magnetization. 



Fig. 21. 



pended needle. Either 
end attracts the same 
pole of the needle, prov- 
ing that it is not mag- 
netized. Fig. 20. To 
prove that a body is a 
magnet there must be 
repulsion between the 
Magnetize the tube of filings by any of the 

Test again with 



^E^ 


,,, 












) 


N 


S 


N 


S 

) 


N 


S 


N 


S 


#' 


) 


$» 


] 



Fig. 22. — Breaking a Steel Magnet. 



body and magnetic needle 

methods previously given, being careful not to shake it. 

the needle; one end 

repels one pole of the 

needle and attracts 

the other pole. The 

filings are now 

located somewhat as 

shown in Fig. 21. 

Now shake the tube thoroughly so as to intermingle the fihngs; repeat the 

tests above, and you find that the tube is no longer a magnet, but has 

been demagnetized. 

Experiment 3. — Magnetize a long, thin piece of tempered steel and 

mark the N-pole. Break 
it in half and test each 
piece separately. In one 
half the N-pole remains 
N, as previously marked, 
but a new S-pole is de- 



N 



n s 


n s 


n s 


n s 


n s 


n s 


n s 


n s 


n s 


n s 


n s 


n s 


n s 


n s 


n s 


n s 


n s 


n s 



Fig. 23. 



Magnified Arrangement of Particles 
in a Bar Magnet. 



veloped, while in the other piece the S-pole remains as before and a new i 

N-pole is developed. Break these pieces again (Fig. 22), and each part is a . 
perfect magnet, with the poles distributed as in the previous case. Break 

the remaining pieces until they become too small to be broken further, j 

Upon test, each piece will still be found to be a magnet. j 

From the above experiments we would infer that a steel or 

iron magnet is an aggregation of small magnets, arranged as ] 

shown in the magnified view given in Fig. 23. . I 



MAGNETISM , 17 

15. Magnetic Saturation. — We cannot see the molecules 
of iron or steel changing their relative positions under the in- 
fluence of magnetism, but these experiments are intended to 
show what probably takes place when steel or iron is magnet- 
ized. According to the theory, the unmagnetized iron or steel 
has its molecules irregularly disposed, as were the steel filings 
in the tube when shaken. Magnetization turns them around 
on their axes until they are arranged symmetrically. When 
they have all been turned around the bar is said to be satu- 
rated, or completely magnetized; it cannot be further in- 
fluenced by magnetism, however strong the force. 

16. The Magnetic Difference between Iron and Steel. — 

Experiment 4. — Insert a bar' of steel in a coil carrying a current of 
electricity; test its attractive power by nails or filings while the current 
is on. Then insert a bar of soft iron of the same size in the coil; test its 
attractive power while the current is on. Now test the attractive power 
of both with the current off. 

The soft iron will be found to possess greater attractive 
force than the steel, when the current is on, while the steel 
possesses far superior attractive properties to the iron, after 
the current is turned off. The iron is magnetized very slightly. 
The magnetism remaining in the iron is known as residual 
magnetism, and is a most important factor in operating genera- 
tors since upon it their self -exciting properties depend. The 
power to retain magnetism is called retentivity. In a steel 
magnet the molecules tend to retain the magnetic position, 
shown in Fig. 21, hence they possess permanent magnetism. 
On the other hand, nearly all the molecules of soft iron tend 
to return to their original position (Fig. 20) when the mag- 
netizing force is removed. The greater the retentivity of a mag- 
netizable body, the more force must be applied to magnetize it. 
The retentivity of steel is much greater than of iron, due to 
the fact that intermolecular friction is greater than in iron. 
. 17. Magnetic Force. — The force exerted by one magnet 
on another, to attract or repel it, or to attract iron filings, is 
termed magnetic force. It is not perceptible to any of the 
senses, but its effects will reveal its existence. When the mag- 
net is plunged into filings, the attraction for them exhibits the 
magnetic force, its direction, and its distribution in the space 



18 



LESSONS IN PRACTICAL ELECTRICITY 



surrounding the magnet. The magnetic force is not the same 
at all distances, but decreases as the distance from the magnet 
increases. 

The magnetic force acts in all directions from a magnet. To 
ascertain the direction of the force in the space surrounding a 

magnet, a small dip 
needle may be used, as 
shown in Fig. 24. 

With the bar magnet 
flat on the table, place 
the dip needle a short 
distance above the 
magnet midway be- 
tween its poles. The 
needle takes up a posi- 
with its N and S poles attracted 
By moving the needle 



X 




y 



Fig. 24. — Exploring the Magnetic Fi^eld 
about a Bar Magnet. 



tion parallel to the magnet, 
by the unlike poles of the magnet, 
toward either pole, the needle will incline toward the magnet, 
the angle of inclination increasing as you approach the pole, 
until it becomes vertical at the pole. If the magnet is laid on 
a sheet of paper, and the dip needle is used to explore its mag- 
netic force by moving the needle slowly from one end of the 
magnet to the other on both ^.^x<-^^ 



sides, the direction that the 
needle points can be recorded 
for each position. The direc- 
tion of the magnetic force 
around the magnet will then be 
approximately as is illustrated 
in Fig. 25, wherein the arrow- 
heads indicate the N-pole of 
the magnetic needle. The figure 
shows that the magnetic force 
has a definite direction at every 
point and that it acts along lines 
called magnetic lines of force. 
18. The Magnetic Field.— 



/ 



.^' 



'^, 



\ 



/; 



"X 






J 



\. 



./ 



.^ 



Fig. 25. — Plotting the Position of 
a Magnetic Needle. 



The space which is permeated 
by the magnetic lines of force surrounding a magnet is con- 
ventionally called the magnetic field of force, or simply a mag- 



MAGNETISM 19 

netic field. It is also assumed that the magnetic, Unes of force 
emanate from the N-pole of a magnet, pass through the sur- 
rounding medium, reenter the S-pole, and complete the path, 
or circuit, from the S-pole to the N-pole, through the magnet 
itself. Every line or curve of magnetic force must have a 
complete circuit; hence, as already proven, it is impossible 
to have a magnet with only one pole. The. magnetic lines 
complete their circuits independently, and never cut, cross, or 
merge into each other. The internal field is much smaller in cross 
section than the external 
field, due to the fact that the 
steel is a much better con- 
ductor of magnetic lines of 
force than the surrounding 
medium. Because of this 
concentration of lines of 
force inside the magnet they 
are crowded together where 
they leave the magnet at 

the N-pole, and where they ^. _^ ^ i,- i ivt .. -p- u 
, ,-, c^ 1 r^<^ Fig. 26. — Graphical Magnetic Field 

enter at the S-pole. ihe of a Bar Magnet. 

strong attraction at the 

poles, and none at the middle of the magnet, is thus ac- 
counted for. 

A graphical representation of the magnetic field surrounding 
a magnet may be produced by placing a sheet of paper over 
the magnet and sifting fine iron filings over the paper while 
gently tapping the paper. The filings, being magnetic bodies, 
arrange themselves in the direction of the magnetic curves or 
lines of force, producing a field similar to Fig. 26. Other mag- 
netic fields, rendered visible by iron fihngs, are shown in Figs. 
27, 28 and 29. 

The student should produce fields similar to Figs. 26 to 29, 
.and of any other possible combinations of magnets that may 
occur to him. A thorough knowledge of the direction of fines 
of force, as depicted by the graphical representations of mag- 
netic fields, will greatly assist in the understanding of the 
phenomena of electromagnetism and electromagnetic induc- 
tion, to be considered later. 




10 



LESSONS IN PRACTICAL ELECTRICITY 



19. Axis and Equator of Bar Magnet. — The straight Une 
joining the N- and S-poles of a bar magnet is called the mag- 
netic axis (Fig. 30). A line 
drawn through the neutral 
point at right angles to the 
axis is called the magnetic 
equator. The neutral point 
may be defined as the posi- 
tion midway between the 
poles where, by the aid of iron 



^^s3:^0y^^iML ^k^ filings, no external magnetism 

-M^^J^Ah'A ,Hv\r^ is shown 




^i^pm^ 



:^,^mmi:m 



W0]r 



f^l 



Field 



is shown. 
20. Magnetic Bodies Free 

to Move. — If a graphical 

Fig. 27. — Graphical Magnetic Field rviao-nptio fiplH bp madp of p 

between Unlike Poles. magnetic neia De maae oi a 

bar magnet with a piece of 
iron lying in the field, it will be noted that the magnetic field 
is distorted, and many of the lines pass through the piece of 
iron. Magnetic lines of force always prefer the path of least re- 
sistance. If a piece of iron is arranged free to move in the field, 
it will turn and take up such a position as to accommodate 
through itself the , ^^^ ^ -^-. . , , . . ,,,,,y .- ,, > 



greatest number of the 
lines of force. The 
fundamental principle 
in many forms of 
electrical measuring 
instruments and elec- 
tromechanical devices 
is that a magnetic 
body, free to move 
under the influence of a 
magnetic field, tends to move so as to accommodate, through itself, 
the greatest number of lines of force of the field. If the movable 
body is a magnet it moves in a particular direction, so that its 
own internal magnetic lines will be in the same direction as 
those of the field in which it is placed. 

21. Magnetic Induction. — A piece of soft iron, placed in 
the magnetic field of another magnet, assumes the properties 




Fig. 28. — Graphical Magnetic Field of Two 
Parallel Bar Magnets with Like Poles Adjacent. 



MAGNETISM 



21 



of the magnet. The iron is the body under induction, the 
magnet the inducing body, 
and the phenomenon is 
known as magnetic induction. 
It may be defined as the 
action and reaction which 
occur when the magnetic fines 
of force, emanating from a 
magnetic body, make evident 
the latent magnetism in 
another magnetic body, 
either with or without con- 
tact of the bodies. The 
phenomenon of magnetic 
induction always precedes the 
attraction of a magnet for a magnetic body, and takes place 
^ .^ through all non- 

/ /^/ r^^— -^— -.7 ""x'^^s"^^ magnetic medi- 

ums, whether they 
are solids, fiquids, 
or gases. Mag- 
netic induction in 
iron may be ex- 
plained by the 
molecular theory, 
when it is remem- 
bered how readily 




29. — Graphical Magnetic 
of a Horseshoe Magnet. 









N -<- 



rnef/c ax/s 



\\\ 



Magnet 



Fig. 30. — • Conventional Field of a Bar Magnet. 

the molecules of soft iron turn on their axes when subjected to 
a magnetizing force. The 
methods of magnetization 
given in H 6 are based on 
the principle of magnetic 
induction, which the stu- 
dent should now apply to 
each case. 

Experiment 5. — Plunge a -m- o. at .• t i 

soft iron bar in iron filings and ^^S- 31. - Magnetic Induction, 

note that no filings are attracted to it. Bring one pole of a magnet in con- 
tact with the iron bar, dip the end of the bar in filings, and note that they 
are now attracted to it. Remove the magnet from contact with the soft 




22 



LESSONS IN PRACTICAL ELECTRICITY 




Bar Magnet 

Soft Iron-' 



Fig. 32. — Magnetic Induction. 

Without the magnet the needle is in the posi- 
tion NS; but when the magnet is brought near 
the rod, the needle is repelled to position N' S'. 



iron; note that, while most of the fihngs drop off, there are still a few that 
cling to the iron. Why? Separate the magnet from the iron bar by pieces 
of wood, brass, glass, etc., apply the iron to the fihngs as shown in Fig. 
31, and observe their attraction; proving that magnetic induction takes 
place between bodies in contact or separated from each other. 

Experiment 6. — Support an iron rod about six inches long, horizontally 
in line with, and on the same height as, a poised magnetic needle when it 
is pointing north and south, but separated from the N-pole of the needle 

by a small space, as in Fig. 32. 
With the N-pole of a bar magnet 
approach the far end of the iron 
rod, and the needle will be repelled 
from the iron rod. The iron rod 
is first magnetized inductively by 
the needle, the N-pole of the 
needle inducing a S-pole in the 
end of the iron nearest to it and a 
N-pole at the far end. The bar 
magnet (the inducing body), being 
stronger than the needle, induces 
a S-pole in the end of the iron nearer to it and a N-pole in the other 
end, thus neutralizing the needle's inductive effect by demagnetizing the 
iron and remagnetizing it in the opposite direction. When the magnetiz- 
ing body is removed the needle assumes its former position, provided the 
iron is very soft. This experiment proves that the bar of iron has poles 
when inductively magnetized. 

22. Magnetic Screens. — Permit a magnet to deflect a 
magnetic needle; then interpose any nonmagnetic substance, 
such as wood, glass, or rubber, between the magnet and the 
needle; the deflection is not altered. A 
plate of thick iron, however, when inter- 
posed between the magnet and the 
needle, acts as a magnetic screen, reduc- 
ing the deflection of the needle toward 
the magnet. The iron plate is magnetized 
inductively by the magnet on the one 
side ; the needle produces a similar effect 
on the other side of the plate and, being 
free to move, deflects slightly, until its 
lines of force are proportionately accommodated between the 
earth's magnetism and the magnetism in the iron plate. There 
is no magnetic insulator, that is a material which will stop the 
lines of force. The method of protecting any device from the 











->r^---Sv^ 


7tx<'j:;-c<\ 


/-y v-\ 


( A ) 


I ^V " //- 1 . . 




_\-'~^^^-"t^'^-''JvL 




^>^i^^>^ 





Fig. 33. — Magnetic 
Screen. 



MAGNETISM 23 

effects of a magnetic field is to use a soft iron screen that would 
encircle the device, thus conducting the lines of force of the 
field around it. Thus in Fig. 33, the circular iron screen B 
carries the magnetic lines of force and leaves the inner region 
A free from such lines. This principle is utihzed in the use of 
heavy cast iron boxes for certain measuring instruments, to 
shield them from the effects of a magnetic field. 

23. Consequent Poles. — Although two poles is the least 
number a magnet can have, it may possess any number greater 
than two. All these poles except the two end poles are called 
consequent poles (Fig. 34). If two 

like poles of a weak and a strong .^'V^J^'^^-^^ 

magnet be approached to each other, /V'_' _ ~^>^^ . 
as a compass needle not free to move \[(y:^^//::::^f;':^:^\;l^y 
and a bar magnet, repulsion will take ~;r| fe''' ' ''' V^;^ ' ' ^"'n ''''' ' ^ ^'i l^;'- 
place up to within a certain distance J-v,^''^c;^?i;v@:';\v 
between the hke poles, after which /' iV^'---'-'' '^---''' ^--'';/'; '^ 

attraction occurs, because the indue- '^O^- -—^^^^y 

tive effect of the stronger magnet ~ '" 

has demagnetized the weaker magnet ^ig^M. - »- M^^gnet^with 
and remagnetized it agam with op- 
position polarity. Magnetic needles often have their polarity 
thus reversed, so that the marked ends point south instead of 
north. In making any tests with a needle always allow it to 
come to rest first in the eartKs field, as the polarity may have 
been reversed since it was last used. 
With a reversal of polarity sometimes more than two poles 
are manifest in the body which has had its 
polarity reversed. In such cases the body 
will have a number of intermediate or con- 
sequent poles and of neutral points; these 
may be readily shown by plunging its entire 
length into iron filings. 
24. Pole Pieces and Armatures. — To 

p _ concentrate and direct the magnetic lines of 

manent Magnet with force, which extend in all directions from the 
Iron Pole Pieces (P) poles of a magnet, pole pieces of soft iron 
and Armature (A) . (j.-^^ 35) ^^^ fastened to the magnet's poles. 
An armature is a magnetic body placed between or near, but 




24 LESSONS IN PRACTICAL ELECTRICITY j 

not touching, the poles of a magnet, and is free to be rotated, | 

as A in Fig. 35, or free to be moved to and from the poles, I 

such as the moving element of a telegraph sounder, or the i 

vibrating arm of an electric bell. ] 



QUESTIONS 

1. "Explain what you mean by the molecular theory of magnetism. 
, Give sketches. 

2. Explain how, by successively breaking' up a bar magnet, you support 
the molecular theory of magnetism. Give sketch. 

3. According to the molecular theory of magnetism, explain what 
you mean by magnetic saturation. 

4. Why is it that hard steel makes a better permanent magnet than 
soft iron? 

5. What do you understand by retentivity? Give an example to 
illustrate your answer. 

6. Two bar magnets with like poles adjacent are laid on a piece of 
cardboard parallel to each other. A horseshoe magnet is placed so that 
its poles are directly opposite but a little distant from the poles of the 
bar magnet. Sketch the resultant magnetic field that you would expect 
to see from this combination if iron fihngs were used. 

7. What is magnetic force? How would you prove its existence and 
direction around a magnetized steel bar? 

8. What is a magnetic field? 

9. A piece of steel attracts the N-pole of a magnet. Would this phe- 
nomenon positively prove that the steel is magnetized? Give a reason 
for your answer. 

10. What is meant by the neutral point of a bar magnet? 

11. Give a concise statement as to the movement of a magnetic body 
(when free to move) when it is placed in a magnetic field. 

12. Cite and illustrate by sketches an experiment to demonstrate the 
phenomenon of magnetic induction. 

13. Apply the principle of magnetic induction to a piece of steel you 
are required to magnetize by rubbing it from one end to the other with one 
pole of a bar magnet. Give sketches illustrating the stages of magnetiza- 
tion. 

14. Upon testing a bar magnet with iron filings it is found to attract 
filings at the center and also at each end. How do you account for this? 
Make a sketch to illustrate your answer. 

15. What is a magnetic screen, and for what purpose is it used? 



LESSON m 
VOLTAIC ELECTRICITY 

Electricity — Electrical Effects — Generation of Electric Currents by 
Chemical Means — A Current of Electricity — Simple Voltaic Cell 
— The Circuit — Conductors and Insulators — Direction of the 
Current — Poles and Electrodes of a Cell — Detector Galvanom- 
eter — Potential and Electromotive Force — Chemical Action in a 
Voltaic Cell — Why the Hydrogen Appears at the Copper Plate — 
Polarization — Table I — On what the Electromotive Force of a Cell 
Depends — The Electrochemical Series — Table II — Local Action — 
Amalgamation — Questions. 

25. Electricity. — The word electricity has been applied to 
an invisible agent known to us only by the effects which it 
produces, or its various manifestations. While the exact nature 
of electricity is not known the laws governing electrical phe- 
nomena are clearly understood and defined, just as the laws 
of gravitation are known, although we cannot define the nature 
of gravity. Electricity was assumed by the early scientists to 
consist of two fluids, which were contained in neutral bodies in 
equal amounts. When by any means this equality was dis- 
turbed in a body, it became charged and electrical manifesta- 
tions occurred. In the light of later scientific knowledge the 
two-fluid theory has been discarded. Faraday believed that 
these manifestations were due to a strained condition in the 
ether which surrounds charged bodies, and this theory of elec- 
tricity was further developed by MaxweU, who considered the 
strain to consist in some sort of displacement in the ether. 

Recent experiments on electrical discharges through gases, 
on radioactivity and on X-rays have shown the inadequacy of 
Maxwell's theory, and have led to its modification which is gen- 
erally known as the electron theory. According to this theory, 
electricity is corpuscular in nature and of one kind only, the 
corpusles being negative charges called electrons. Following 
this theory, a neutral body has a normal supply of electrons, 

25 



26 LESSONS IN PRACTICAL ELECTRICITY 

a negatively-charged body has an excess of electrons, and a 
positively-charged body has a deficiency of electrons. Further, 
the flow of electricity between two points is generally con- 
sidered as a transfer of electrons from one point to the other. 
The flow of electricity through a wire is therefore analogous to 
the flow of water through a pipe, so that electricity can be said 
to flow through a wire. 

26. Electrical Effects. — The manifestations produced by 
electricity may be divided into two distinct classes. First, elec- 
tricity when at rest is known as static electricity, and the bodies 
electrified are said to be statically charged ; the term electrostat- 
ics applies to this subject. Second, electricity in motion differs 
from static electricity and is treated as a current of electricity. 

Electricity in motion produces magnetism, which has been 
termed electromagnetism, it dissociates chemical solutions, which 
has been termed electrolysis, it produces heat in wires, and occa- 
sions other effects, such as electrical waves, etc. All these phe- 
nomena are very intimately associated with each other, and are 
due to the one invisible agent, electricity. In this book we will 
limit the study to currents of electricity and their effects, which 
form the basis of a great many practical electrical applications. 

27. Generation of Electric Currents by Chemical Means. — 

Experiment 7. — Fill a tumbler two-thirds full of dilute sulphuric acid 
(one part acid to twenty parts water) and partially immerse in the solu- 
tion a strip of sheet zinc, say one inch wide by five inches long. Bubbles 
of gas immediately collect on the zinc, and then, 
detaching themselves, rise to the surface of the 
liquid, being rapidly replaced by other bubbles as 
the action continues. These bubbles of gas are 
hydrogen (one of the gases of which water is com- 
posed), and when collected, by displacing water in 
an inverted test tube held over them, this gas may 
be ignited and will burn with a pale bluish flame. 
If the zinc remains in the acid for some time, it 

Y[cr 36 Copper wastes away or is dissolved in the liquid. 

and Zinc in Acidu- Experiment 8. — Place a strip of copper, of about 
lated Water. the same dimensions, partially in the acid as before. 

No bubbles of gas are seen rising from the copper. 
If this metal is allowed to remain for some time it will not apparently be. 
acted upon by the acid. 

Experiment 9. — Place the strips of copper and zinc in the tumbler of acid, 
not permitting them to touch each other, in or out of the liquid . Hydrogen 




VOLTAIC ELECTRICITY 



27 



gas continues to rise from the zinc as before, but there is no action on the 
copper plate. Bring the outer extremities of the copper and zinc strips 
into contact (Fig. 36), and torrents of bubbles are now seen to rise from the 
copper strip, in addition to the bubbles rising from the zinc strip. If 
collected, the gas evolved from the copper proves to be hydrogen, the 
same as that rising from the zinc. If the action is permitted to continue 
for some time, upon examination the zinc is found to have wasted away, 
while the copper remains unchanged. Break the external contact between 
the plates and the action at the copper instantly ceases, but the zinc wastes 
away as before. 

Experiment 10. — Remove the zinc strip from the liquid, and while 
it is stiU wet with the acid rub over its surface a little mercury. Upon 
being replaced in the solution the acid does not attack it. Repeat Ex- 
periment 9 with this " amalgamated zinc " (see 1[42), and note that now 
bubbles rise only from the copper plate, when the ends of the two strips 
are brought together, and that none rises from the zinc plate, but that it 
is still the zinc plate which wastes away. 

Experiment 11. — Connect wires of any metal to the copper and zinc 
plates, being sure that you have bright metalhc contacts. Bring the ex- 
tremities of these two wires together after they have been brightened 
and hydrogen gas is seen to rise from the copper plate as before, while 
there is no action at the zinc. 



When the wires are separated the action ceases, but com- 
mences again as soon as con- 
nection is made. Interpose 
between the two connecting 
wires pieces of glass, mica, 
rubber, paper, wood, porce- 
lain, etc., or connect the two 
plates by a bridge made of 
any of these materials; no 
action appears at either plate. 

It thus requires a connec- 
tion between the two plates 
to cause chemical action, and 
this connection must be of a 
•particular kind. It would 
seem that the plates exert 
an influence upon each other through the connecting wire. We 
will now ascertain whether the connecting wire possesses any 
extraordinary qualities when thus connected with these dis- 
similar plates. 




Fig. 37. — Deflection of a Magnetic 
Needle by a Current Flowing in a Wire. 



28 LESSONS IN PRACTICAL ELECTRICITY ' 

Experiment 12. — Set up a poised magnetic needle. When pointing j 
north and south place above and parallel to it a portion of the connecting ■ 
wire used in the last experiments (as in Fig. 37) . i 

When the ends of the wires are brought together the needle i 

immediately turns upon its axis at right angles, or nearly so, | 

to the wire, after a few vibrations, and remains in this position • 

until the connection is broken, when it assumes its normal ',, 

position. The deviation of the needle from its original position , 

is termed the deflection of the needle. Note that chemical action i 

continued in the tumbler as long as the needle was deflected, ; 

and at the expense of the zinc rod. • 

Experiment 13. — With the wire arranged as in Experiment 12, inter- | 
pose pieces of tin, steel, copper, iron, lead, gold, brass, aluminum, etc., ! 
between the connecting wires, and the needle is deflected as before. When ; 
pieces of paper, glass, wood, mica, etc., are interposed, however, there is 1 
no deflection of the needle, which again proves the necessity of a suitable j 
connector between the copper and zinc plates. \ 

Experiment 14. — Test an iron rod by iron filings for magnetism. It ■ 
does not attract them. Wind a few turns of cotton-covered wire around ; 
the iron rod and plunge it into the filings, after first connecting the ends ; 
of the wires to the two plates in the tumbler. Filings are now attracted i 
to the iron core, but drop off when the connection to the plates is broken, i 
This, then, is a temporary magnet, produced by the magnetic properties ' 
possessed by the wire. | 

28. A Current of Electricity. — From the foregoing experi- ! 
ments it appears that when zinc and copper are immersed in \ 
an acid solution and connected by a wire, the wire possesses \ 
unusual magnetic properties. The cause of this magnetic j 
effect, and other effects associated with it to be noted later on, j 
is attributed to electricity, and the property possessed by the ; 
wire is said to be due to a transference of electricity from one \ 
plate to the other, the wire acting as a conducting medium. ; 
When we speak of a current '' flowing through the wire from | 
plate to plate," it is simply a convenient expression used to \ 
describe the phenomena involved, although we may not know \ 
what actually transpires. . i 

An ebonite or glass rod is electrified when rubbed with flannel, ] 
silk, etc., and possesses the power of attracting light bodies j 
to it, and also of attracting or repelling another similarly elec- j 
trifled rod, according to the nature of its electrification. When | 
the portion of a rod so electrified is touched by the hand, or i 



VOLTAIC ELECTRICITY 29 

other conductor, the electrification disappears and the body 
is said to be discharged. The two plates in the tumbler may 
be said to be electrified to different degrees of electrification, 
and when they are connected by a wire, the electrification 
discharges from the higher to the lower electrified plate. The 
action of the acid upon one plate more than the other, however, 
tends to keep the plates at different states of electrification, 
and the successive discharges through the connecting wire 
become so intensely rapid that they form practically a con- 
tinuous current of electricity. 

29. Simple Voltaic Cell. — When two dissimilar metals are 
partially immersed in a solution, which is capable of acting 
chemically upon one of them more than upon the other, the 
combination constitutes a voltaic cell. The name voltaic is 
derived from an Itahan physicist, Volta, who first discovered 
the cell in 1800. It is sometimes called a galvanic cell, after 
Volta' s contemporary, Galvani. Correctly speaking, the word 
battery applies to a number of such cells connected together, 
though the name is commonly applied to a single cell. The 
solution in which the metals are immersed is called the elec- 
trolyte, or exciting fluid, or excitant. The term primary cell is 
generally used to signify any cell that generates an electric cur- 
rent directly from the chemical action of an electrolyte on two 
dissimilar materials. 

30. The Circuit. — Considering again our shnple voltaic 
cell (Fig. 37), the term circuit is applied to the entire path 
through which the transference of energy takes place, or the 
current of electricity is supposed to flow, and the wire joining 
the plates is called the conductor. The circuit, then, consists 
of not only the conductor between the plates outside of the cell, 
but the liquid conductor between the plates inside of the cell; 
hence we speak of the external circuit and the internal circuit. 

The complete circuit includes the conducting wire, the two 
plates which act as conductors, and the liquid between them. 
Bringing the two extremities of the wires into contact is called 
making, or closing the circuit, and separating the wires is termed 
opening, or breaking the circuit. 

31. Conductors and Insulators. — The substances which, 
when interposed between the terminal wires of a voltaic cell, 



30 



LESSONS IN PRACTICAL ELECTRICITY 



do not interfere with the deflection of the magnetic needle 
(as the metals) are known as conductors of electricity, because 
they allow the current to flow through them, while other sub- 
stances so interposed, as glass, wood, mica, etc., interfere 
with the action in the cell and upon the needle, and are there- 
fore called insulators. All substances resist, or oppose, the 
flow of electricity, those substances known as conductors (as 
the metals) offering considerable less opposition than those 
classed as insulators. This opposition is termed electric resist- 
ance (II 62), the amount of electric current depending upon the 
resistance in the circuit, as well as upon the electromotive 
force (T[ 35). A classified list of conductors and insulators is 
given in 1[ 64. 

32. Direction of the Current. — 

Experiment 15. — Place the conducting wire of a voltaic cell over and 
parallel with a magnetic needle when it is pointing 
^N north and south (north is at the left in Fig. 38). 

^j^ *Ny Close the circuit and note whether the N-pole of 
,^,;#i=^^ ) the needle points east or west when the current 

* I ^y is flowing. Say it is deflected to the east. Now 

reverse the wire connec- 
tions at the battery plates 
(that is, connect the end of 
the wire which was at- 
tached to the zinc to the 
copper, and vice versa); 
the N-pole of the needle 
now points west if the wire 
is held as before, Fig. 39. 

This experiment indicates that electricity 
produces a magnetic force around a wire. Fig. 
and, on account of the behavior of the 
needle, that this force has direction. In consequence the flow 
of electricity has direction. Electricians have agreed to assume 
that the electricity flows from the co'pyer terminal to the zinc 
terminal through the conducting wire, and from the zinc plate to 
the copper plate through the solution. 

33. Poles and Electrodes of a Cell. — The metal plates or 
elements suspended in the liquid, are termed the plates, or 
electrodes, and the conducting liquid the electrolyte. The 
copper plate is called the negative plate or electrode, and the 



>" 



Cu 



Zn 



Fig. 38. — Direction 
of Current Flow. 




39. — Direction 
of Current Flow. 



VOLTAIC ELECTRICITY 



31 



zinc plate the positive plate or electrode, while the external end 
of the copper plate is called the positive pole, and the exter- 
nal end of the zinc plate, the negative pole (Fig. 40). If we 
bring the + (plus- sign for the 
positive) and - (minus sign for 
negative) wires from a cell together 
making the circuit, the current 
passes from the + (copper) to the - 
(zinc) terminal across the junction, 
and also from the + plate (zinc) 
to the - plate (copper) through 
the cell. In any electro-generative 
device that pole is considered posi- t^QgaUve 
live from which the current flows, Plate" 
and that pole negative to which the Electrode 
current flows. As an aid in remem- 
bering the terminals or poles con- 
sider the chemical abbreviation 




Fig. 40. — Nomenclature of a 
Voltaic Cell. 



for zinc, namely Zn and that the 
word negative begins with the letter 
n. In any cell the positive plate (generally zinc) is the one most 
acted upon, the current being supposed to start at the surface 
of this plate, travel through the solution to the copper plate, 
and from the copper terminal to the zinc terminal through the 
external circuit. 
34. Detector Galvanometer. — 

Experiment 16. — From Experiment 15 it was seen that if a current 

passes over a needle it is deflected to the east or west, according to the 

, direction of the current. 



The student should now 
prove that the needle is 
deflected oppositely if the 
wire be held underneath, 
but parallel to it, according 
to the direction of current 
in the wire. Note also that 
for the same direction of cur- 
rent underneath the needle 
as above it, the deflection is opposite to what it previously was. Now bend 
the wire around the needle, at rest, parallel to it, so that the current flows 
over the needle and under the needle in opposite directions. The deflection 
is now in the same direction, and greater than before. Make several con- 



Fig. 41. 



Simple Form of Detector Gal- 
vanometer. 



32 LESSONS IN PRACTICAL ELECTRICITY 

volutions (Fig. 41) and the deflection is further increased. A few turns of 
wire wrapped around a pocket compass, parallel to the needle when it is 
pointing north and south, constitutes a simple form of detector galvanometer, 
and when inserted in a battery circuit will indicate by the deflection of 
the needle that a current is flowing. Various types of galvanometers are 
described in Lesson XVI. 

35. Potential and Electromotive Force. — Suppose two 

vessels partially filled with water are joined by a pipe and that 

the water is at the same level in both. The connecting pipe is 

full of water, yet there is no current of water flowing through 

^^===^^^ the pipe because the pressure at 

1^ ^^^^^ each end is the same. When one 

I ^~^m vessel, A (Fig. 42), is raised above 

^ V- M^ ^^^ other, B, then there is a differ ^ 

^ ^""^^^^^^Sito^ ^^^^ ^^ pressure between the two 

I ^^"^^^^^ &n.d^ of the pipe, and a current of 

I ^hI^^ water flows from the higher to the 

^ ^^^ lower level, due to this difference 

B W — ^0 ^^ pressure (or head) between the 

\|_ pM two points. It is not necessary to 

^-^^ know the height of vessel A or B 

^'^- fotTn'illDktnlr '" above the sea level, but the height 

or head, H, between the two ves- 
sels. Similarly, if two points on a copper bar are elevated to 
the same temperature there is no transference of heat from 
one point to the other. If, however, one point is at a higher 
temperature than the other, there is then a difference in tem- 
perature between the points and a transference of heat from 
the point of higher to the point of lower temperature. 

The word 'potential as used in an electric sense is analogous 
to pressure in gases, head in liquids, and temperature in heat. 
In the voltaic cell, then, we have two bodies raised to different 
electrical potentials (see 1[ 28) , and to the difference of potential 
between them is due the current flowing through the wire con- 
necting the plates. The greater this difference of potential 
the greater the current, or effect of the current produced. 

Potential is the force which moves electricity through the 
circuit. The total force required to cause the current to flow 
through the entire circuit is called the electromotive force, 
whereas a difference of potential would exist between two points 



VOLTAIC ELECTRICITY 33 

in a circuit, which would cause the current to flow just between 
these two points. Electromotive force (abbreviated E. M. F.) 
is the total difference of potential (abbreviated P. D.) that 
is maintained in any circuit. 

Experiment 17. — Insert two similar pieces of copper or of zinc in the 
tumbler of acidulated water and test for a current by a detector galvanom- 
eter. The needle is not deflected. The similar plates being both elec- 
trified to the same degree, there is no difference of potential between them, 
hence no current. This is analogous to the two vessels of water placed on 
the same level. 

36. Chemical Action in a Voltaic Cell. — A continuous 
potential difference is maintained between the zinc and copper 
electrodes of a voltaic cell chiefly by the action of the exciting 
Hquid upon the zinc. The chemist symbohzes sulphuric acid 
as H2SO4, meaning that it is composed of two parts hydrogen 
(H2), one part sulphur (S), and four parts oxygen (O4). The 
SO4 part of the acid has a strong affinity for the zinc, and when 
the cell circuit is completed, attacks the zinc and forms zinc 
sulphate (ZnS04), which is dissolved in the water. For every 
SO 4 part of the sulphuric acid which unites with the zinc, two 
parts of hydrogen gas are liberated, which escape from the solu- 
tion as already noted in the experiments. The zinc thus re- 
places the hydrogen in the acid, setting it free. The chemical 
action may be expressed as follows : 

Zn + H2SO4 = ZnS04 + . H2. 

Zinc and sulphuric acid produce zinc sulphate and hydrogen. 

Every time the circuit of a cell is completed, and as long 
as it is completed, this chemical action takes place, the zinc 
gradually wasting away; also the power of the acid to attack 
the zinc gradually becoming exhausted. Thus the electrical 
energy is maintained in the external circuit to perform use- 
ful work by the expenditure of so many pounds of zinc and 
acid inside the cell. In other words, the combination of zinc 
with the acid radical, SO4, of the sulphuric acid liberates energy 
which manifests itself as an electric current in the circuit. 
The chemical energy of the voltaic cell is changed into elec- 
trical energy somewhat hke the chemical energy contained in 
a lump of coai is converted into kinetic energy when burned 
under a steam boiler. 



34 



LESSONS IN PRACTICAL ELECTRICITY 



37. Why the Hydrogen Appears at the Copper Plate. — As 

already stated, when zinc is immersed in sulphuric acid, hy- 
drogen is liberated and rises in bubbles to the surface of the 
solution. In the voltaic cell it was noticed that the hydrogen 
bubbles rose from the copper, yet no bubbles were seen to pass 
through the solution. Many chemists believe that the instant 
an element is liberated from a compound (as the H2 from the 
H2SO4) it possesses unusual readiness to enter into combination 
with other molecules. The action that takes place in a cell 
may be pictured as follows : at the instant the circuit is closed 



Cu 



Free 

( + ) 



Free 
(-)■ 



Balvanomefer 



Cu 




/ 



=^^ 



^:^BeforeA ction No Curren f - . 



Zn Cu 



Copper,D I lute Sulphuric Acid and ZlnC' 




Cu 



■ During Action _^ Currenf_ Passing 



In 

Copper -iDiiuieSulphuncV Zinc " 2inc 

Hydrogen^ - - > ^- 

^///////////////////////////////////yy///////////////^ 



Fig. 43. — The Chemical Action in a Voltaic Cell when the Circuit ] 
is Closed. i 

The molecules of sulphuric acid are represented by the ovals. 

(Fig. 43) the SO4 of molecule 1 unites with a molecule of zinc, ; 
setting free a molecule of hydrogen; this instantly unites with ! 
the SO 4 of molecule 2, forming a new molecule of H2SO4 and | 
setting free the Ii2 of molecule 2. This action continues until | 
the last free molecule of H2 appears at the copper plate and j 
rises to the surface. | 

38. Polarization. — \ 

Experiment 18. — Connect a voltaic cell to a detector galvanometer | 
wound with a few turns of wire and note the angle of deflection of the j 
needle. Allow the current to flow for a while, and note that the deflection | 
gradually falls and becomes much less than at first. Brush off the bubbles j 
adhering to the copper plate with a swab and the deflection is increased, 
thus indicating a stronger current; but it soon falls again when the copper 
plate becomes coated with the hydrogen gas. 

The copper plate coated with hydrogen becomes practi- 
cally a hydrogen plate. Now the effect of using a plate of 



VOLTAIC ELECTRICITY 35 

hydrogen with zinc in a cell would be to set up a current from 
the hydrogen to the zinc inside the cell and from the zinc to 
the hydrogen outside of the cell. As this tendency acts 
against the direction of the ordinary copper-to-zinc current it 
weakens the current from the cell. When the cell becomes 
weakened in this manner by a coating of hydrogen bubbles on the 
negative plate it is said to be polarized and the phenomenon 
is called polarization. Polarization, then, must be properly 
overcome by arresting the bubbles in some manner, in order to 
permit the cell to give a strong current as long as any zinc 
remains to be acted upon. The employment of different 
methods of preventing polarization has resulted in the numer- 
ous types of cells now on the market. 

The following test made on a Leclanche cell (1[54) will illustrate the 
phenomenon of polarization. The cell was connected to a circuit of low 
resistance, and readings of a voltmeter ( ^ 129) were taken at one-minute 
intervals for five minutes, during which time the E. M. F. dropped from 
1.41 to 0.63 volts. The cell was then allowed to stand on open circuit for 
five minutes, and then one-minute readings were taken to note its recupera- 
tion. At the end of the fifth minute the former E. M. F. was not regained, 
but only 1.18 volts. One-half hour after the test a measurement showed 
the original E. M. F. of 1.41 volts. 







Table I. 


Polarization Test 






Discharge 




Recuperation 


minutes 


1.41 volts 


minutes 


0. 63 volts 


1 




1.03 " 


1 




0.87 " 


2 




0.80 " 


2 




0.97 " 


3 




0.70 " 


3 




1.06 " 


4 




0.65 " 


4 




1.14 " 


5 




0.63 " 


5 




1.18 " 



39. On what the Electromotive Force of a Cell Depends. — 

If two plates of zinc are immersed in an acid solution (Experi- 
ment 17) and connected, there is a tendency to produce oppo- 
site currents, which neutrahze each other; since there is no 
xiifference of potential between them, no current flows. The 
essential parts of any cell, then, are two dissimilar metals im- 
mersed in an acid solution, one of which is more readily acted 
upon hy the acid than the other. The greater the difference in 
intensity of chemical action the greater the difference of poten- 
tial, and the greater the current strength. 



36 LESSONS IN PRACTICAL ELECTRICITY 

Other metals than copper and zinc may be used in cells, 
and as acids attack the different metals with varying intensi- 
ties of chemical action, some combinations will produce better 
results than others. For example, a cell composed of zinc and 
lead plates, immersed in dilute sulphuric acid, will not deflect 
a magnetic needle to so great an angle as a zinc-copper cell 
of the same size, because a higher difference of potential 
is set up between zinc and copper than between zinc and lead. 

The electromotive force of a cell is dependent also on the 
solution used to attack the zinc, so that the same battery 
plates immersed in different acids would indicate different 
potential differences for the combination in the various solu- 
tions. Using the same solution, however, this force is inde- 
pendent of the size of the plates, a small battery having the same 
potential difference, or E. M. F., as a large one of the same kind. 

40. The Electrochemical Series. — In the following hst of 
substances, known as the electrochemical series, those most 
acted upon (electropositive plates) by dilute sulphuric acid 
are placed at the left-hand of the list, while those least acted 
upon (negative plates) are placed at the right-hand end of the 
list. The arrangement would be different for other acids used 
as electrolytes. 

Table II. The Electrochemical Series 

Direction of current through external circuit 



N A 





5r! 




B 


a 


1 


O 


g 

r^ 


.2 


o 


H-^ 


O 


m 


S 


O 



Positive a ^ § o Negative 

plates « g^l ^1"^'§ plates 



Direction of current through solution 

The difference of potential in a lead-silver cell would be 
less than in a lead-carbon cell, while an iron-carbon cell would 
have a greater P.D., and a zinc-carbon cell still greater. For 
this reason zinc and carbon, being cheap materials, are ex- 
tensively used in batteries. The arrows indicate the direction 
of current through the internal and external circuits. In 
a lead-carbon cell the carbon would be the positive and the lead 



VOLTAIC ELECTRICITY 37 

the negative terminal; while in a lead-zinc cell the lead is the 
positive terminal and the zinc the negative terminal. Con- 
sidering the plates in the Hst, any substance is positive to any 
substance which follows it and negative to any ^preceding it. 

Experiment 19. — Using similar-sized strips of lead, copper, carbon, and 
zinc, make up some different cells with dilute sulphuric acid. Connect each 
combination to the detector galvanometer and note the direction that 
the needle swings, the value of the deflection, and to which terminal each 
plate was connected. Note that when lead is connected to the same 
terminal of the galvanometer, and carbon used with it, the deflection is in 
the opposite direction to that when zinc is used with lead, which illustrates 
that in one instance the current leaves the lead terminal (+), and in the 
other instance flows to it (— ). 

Experiment 20. — Connect a galvanometer wound with many turns 
of fine wire to a voltaic cell and note the value of the needle's deflection. 
Slowly withdraw the plates from the liquid and you note that the deflection 
of the needle remains the same until the circuit is broken at the surface 
of the liquid. This proves that the E.M. F. is independent of the area of 
the plates immersed (see 1[39). Move the plates farther apart or closer 
together and the deflection is not changed, if the galvanometer is wound 
as above. The E. M. F. of a cell is independent of the distance between 
the plates. 

Experiment 21. — Perform Experiment 20 again, using a galvanom- 
eter wound with a few turns of comparatively heavy wire instead of the 
one with many turns of fine wire. 

Note in this experiment that when you slowly withdraw the plates 
from the hquid that the deflection of the needle decreases, for this type 
of galvanometer indicates the amount of electric current instead of the elec- 
tric pressure, as in Experiment 20. With the voltaic cell still connected 
to this galvanometer move the plates further apart, and the deflection 
decreases; move the plates closer together and the deflection increases. 

The amount of electric current that will flow from a cell, then, is depend- 
ent upon the area of the plates immersed and the distance between them. 

41. Local Action. — When a pure piece of zinc (difficult 
to obtain) is used in a cell there is no action at the zinc except 
when the cell is in use. The ordinary commercial zinc con- 
tains many impurities, such as small particles of carbon, iron, 
tin, lead, etc., and when a rod of such zinc is placed in a cell 
these foreign particles form numerous local voltaic cells on the 
surface of the zinc inside the cell, with the result that the zinc 
is being continuously eaten away, whether the cell is in action 
or at rest. These small currents divert just so much strength 
from the regular battery current, thereby weakening it. Fig. 44 



38 



LESSONS IN PRACTICAL ELECTRICITY 



( T =1 I Solufion 




illustrates a magnified particle of iron on a zinc rod, and a 
local current would flow from the zinc to the iron through the 
solution and from the iron to the zinc 
across the junction. This is known as 
local action. In some cells local action 
is also caused by a difference in the 
density of the Uquid at various parts 
of the cell. In this case the zinc near 
the top of the liquid is ordinarily 
wasted away and may be entirely eaten 
off. 

42. Amalgamation. — Local action 
may be prevented by thoroughly clean- 
ing the zinc with sandpaper, then im- 
mersing it in dilute sulphuric acid, and while still wet applying 
mercury (quicksilver) by means of a rag swab. A bright amal- 
gam is formed over the surface of the zinc and it is said to be 
amalgamated. The foreign particles in the zinc are either pro- 
tected from the action of the acid, or are carried down to the 
bottom of the cell. The mercury does not prevent the zinc from 
being dissolved during the action of the cell, but continues to 
re-form an amalgam as the zinc wastes away. * Zinc for battery 
plates is sometimes cast with a small percentage of mercury 
in its composition. 



Fig. 44. — Local Action. 



QUESTIONS 

1. Explain what you understand by the word electricity. 

2. How does electricity manifest itself? 

3. What is the action of dilute sulphuric acid on zinc? 

4. What is a simple cell? 

5. Explain the action in a simple voltaic cell. Give sketch. 

6. Give your idea of a " current " of electricity. 

7. What is an electrolyte ? 

8. What is meant by an open and and by a closed circuit? 

9. Distinguish between the internal and external circuit of a cell 

10. What is a detector galvanometer, and for what purpose is it 

11. What are insulators? 

12. What is meant by a good conductor? 

13. State an experiment you would make to determine whether a 
was an insulator or a conductor. 

14. Give a reason for attributing direction to a current. 



used? 
body 



VOLTAIC ELECTRICITY 39 

15. Which way does a current flow inside a voltaic cell? 

16. Sketch a simple voltaic cell, name all the parts, and show the direc- 
tion of the current in the internal and external circuits. 

17. Distinguish between poles and plates. 

18. Which is the negative electrode in a lead-copper cell using H2SO4? 

19. Which is the positive plate in a lead-iron cell using sulphuric acid? 



LESSON IV 
PRIMARY CELLS 

Primary Cells — Open-Circuit Cells — Closed-Circuit Cells — Remedies 
for Polarization — The E. M. F. of Cells — Smee Cell — Bichromate 
Cell — Fuller Bichromate Cell — Partz Acid Gravity Cell — Bunsen 
and Grove Cells — Daniell Cell — Leclanche Cell — Gonda Leclanche 
Cell — Carbon Cylinder Cell — Edison-Lalande Cell — Weston Stand- 
ard Cell — Dry Cells — Classification of Primary Cells — Chemicals 
for Cells and Some Chemical Symbols — Questions. 

43. Primary Cells. — Primary cells are composed of two dis- 
similar metals or materials immersed in an acid solution (U 29) 
which acts chemically on one of the metals or materials more 
readily than it does on the other. Through this difference in 
chemical action on the two materials, an E. M. F. is maintained 
which will force an electric current through an external circuit. 
Thus, the chemical energy is converted into electrical energy; 
the positive electrode, generally zinc, being consumed or used 
up in producing the current. When the zinc has all been 
consumed, the cell can be renewed by putting a new zinc and 
fresh electrolyte in the cell, after which it is again ready to 
furnish a current. 

There are other cells, known as secondary cells (storage 
batteries or accumulators, Lesson XII), which can be renewed 
without adding new electrolyte or plate material — they are 
restored to their original state by sending a current through 
them in a direction opposite to the current supplied by the cell. 

A good primary battery should have the following qualifica- 
tions: 

Its electromotive force should be high and constant. 

Its internal resistance (^ 72) should be small. 

It should give a constant current; therefore it must be free 
from polarization and not liable to rapid exhaustion. 

It should be inexpensive and of durable materials. 

It should be perfectly quiescent when its circuit is open. 

40 



PRIMARY CELLS 41 

Primary cells are divided into two general classes, according 
to the manner in which they are to be used, namely o'pen- 
circuit cells and closed-circuit cells. 

44. Open-Circuit Cells. — Open-circuit cells are used for 
intermittent work, where the cell is in service for short periods 
of time, such as for electric bells, telephony, and electric gas 
Ughting. In cells of this class polarization does not have much 
opportunity to occur, since the circuit is closed for such a short 
period of time; hence, these cells are always ready to deliver a 
strong current when used intermittently. If kept in continu- 
ous service for any length of time the cell soon polarizes or 
" runs down," but will recuperate after remaining on open cir- 
cuit for some httle time. 

45. Closed-Circuit Cells. — In the closed-circuit type of cell 
polarization is "prevented by chemical action, so that the cur- 
rent will be constant and steady till the energy of the chemi- 
cals is nearly expended. This type of cell is adapted for fur- 
nishing current continuously, as in the service of small lamps 
and motors, telegraphy, fire-alarm signals, electroplating, etc. 

46. Remedies for Polarization. — In the simplest form of 
cell, using zinc, copper and dilute sulphuric acid, no attempt 
has been made to prevent polarization (1[38); hence it will 
quickly polarize when the circuit is closed for any length of 
time, and may be classified as an open-circuit cell. When 
polarization is remedied by chemical means the chemical added 
is one that has a strong affinity for hydrogen and will com- 
bine with it, thus preventing the covering of the negative plate 
with the hydrogen gas. The chemical used for this purpose 
is called the depolarizer and may be used either in a solid or liquid 
form. This choice gives rise to several forms of cells, such as 
cells with a single fluid, containing both the acid and the de- 
polarizer; cells with a single exciting fluid and a solid depolar- 
izer; and cells with two separate fluids. (See 1[ 60.) 

- In the double-fluid form of cell the zinc is immersed in the 
liquid (frequently dilute sulphuric acid) to be decomposed 
by the action upon it, and the negative plate is surrounded by 
the liquid depolarizer, which will be decomposed by the hydro- 
gen gas it arrests, thereby preventing polarization. The two 
liquids are sometimes separated by a porous partition of un- 



42 



LESSONS IN PRACTICAL ELECTRICITY 



glazed earthenware, keeping the Uquids from mixing, except 
very slowly, but not preventing the passage of hydrogen or 
electricity. 

Experiment 22. — Place sufficient mercury in a small battery jar to 
cover the bottom and fill the jar with a sal-ammoniac solution. Suspend 
a piece of zinc from the top of the jar and you have a zinc-mercury cell. 
Make the connection with the mercury by a piece of rubber-covered wire. 
Connect the cell to a current galvanometer and note the decreasing deflec- 
tion of the needle, due to polarization. When the cell becomes sufficiently 
polarized drop into the solution a piece of mercuric chloride (HgCl2) the 
size of a pin-head. The galvanometer needle instantly shows a much 
larger deflection. The hydrogen has been removed by the chlorine in the 
riiercuric chloride. When the chloride becomes exhausted polarization 
sets in again. The mercuric chloride is thus a chemical depolarizer. 

47. The E. M. F. of Cells. — Considering the electromotive 
force of one particular type of cell as a standard of E. M. F., 
another type of cell will possess either a greater or less force 
in comparison with it. The unit of electromotive force is 
called the volt, and is about the pressure set up by a Daniell 
cell, so that if a cell has an E. M. F. of 1.4 volts we mean that 
it possesses 1.4 times the force of a Daniell cell. Cells are, 
therefore, rated by their E. M. F. In ^ 102 will be found a 
table of E. M. F.'s of the different types of cells. 

48. Smee Cell. — The Smee cell, Fig. 45, utilizes mechanical 
means to overcome polarization. A plate of lead or silver is 

suspended between two zinc plates in dilute 
sulphuric acid. The silver or lead plate is 
covered with a fine, powdery deposit of plati- 
num, which gives the surface a rough character, 
so that the bubbles of hydrogen will not readily 
adhere to it as they are formed, but rise to the 
surface of the solution. Another mechanical 
method to overcome polarization is to rotate 
the electronegative plate, thus preventing bub- 
bles of gas from adhering to it; but as this 
necessitates a constant force to keep the plate 
in motion, the cell would not be very econom- 
ical. No mechanical method can wholly pre- 
vent the collection of hydrogen on the negative 
plate. This can only be accomplished by furnishing some 




Fig. 45. — Smee 
Cell. 



PRIMARY CELLS 



43 



chemical with which the hydrogen, as soon as it is Hberated, 
will combine. The E. M. F. of a Smee cell is about 0.65 volt. 

49. Bichromate Cell. — In the bichromate cell polarization is 
prevented by chemically arresting the hydrogen gas, so that 
it never reaches the negative plate. The same will be true of 
most of the ceUs now to be described. Bichromate of soda 
or bichromate of potassium is the depolarizer, to which is 
added water and sulphuric acid for attacking 
the zinc. The bichromates are rich in oxygen, 
for which hydrogen has a strong affinity. 
Carbon and zinc plates are used, and this 
type is made up in several forms termed 
chromic acid cells. 

In the Grenet (Gren-a') form a zinc plate 
is suspended by a rod between two carbon 
plates. Fig. 46, so that it does not touch 
them, and/ when the cell is not in use the 
zinc is withdrawn from the solution by rais- 
ing and fastening the rod, a, by means of a 
set-screw, as the acid attacks the zinc when 
the cell is on open circuit. This cell has an 
E. M. F. of over 2 volts at first, and gives 
a strong current for a short time, but the p-^ ^q 
liquid soon becomes exhausted, as will be 
indicated by the gradual change in the color 
of the solution from an orange to a dark 
red. The zinc should be kept well amalgamated and out of 
the solution, except when in use. It is a good type of cell 
for experimental work, and about two cells would perform a 
large number of the experiments in this book. A simple sub- 
stitute for this cell would contain a number of electric-hght 
carbons fastened together to form the negative plate and 
several zinc rods for the positive plate, the latter could be 
Temoved at will and then rinsed in water. 

To make a solution for a bichromate cell take 3 ounces of 
finely powdered bichromate of potash and 1 pint of boiling 
water; stir with a glass rod, and after it is cool add slowly, 
stirring all the time, 3 ounces of sulphuric acid. The solution 
should not be used until cool. In mixing a battery solution 




Cell. 



Grenet 



Zinc and carbon in 
bichromate solution. 



44 



LESSONS IN PRACTICAL ELECTRICITY 




always jpour the acid gently into the vjater, while stirring, to dis- 
sipate the heat. Never pour water into add. If bichromate 
of soda is used as above, take 4 ounces of bichromate of soda, 
1 J pints of boiling water, and 3 ounces of sulphuric acid. These 
battery solutions are sometimes termed electropoion fluids. 

50. Fuller Bichromate Cell. — The Fuller double-fluid cell has 
the advantage over the Grenet type, in that the zinc is always 

kept well amalgamated and does 
not require removal from the 
solution. A pyramidal block of 
zinc, to which a metalhc rod 
covered with gutta-percha is at- 
tached, is placed in the bottom 
of a porous cup (Fig. 47) and an 
ounce of mercury is poured in. 
The cup is filled with a very 
dilute solution of sulphuric acid 
and water, and then placed in a 
glass or earthen jar containing 
the bichromate solution and the 

carbon plate. The acid diffuses through the porous cup rapidly 

enough to attack the zinc, which, being well amalgamated, 

reduces local 

action. The hy- 
drogen travels 

from the zinc 

through the 

porous cup and 

combines with 

the oxygen in 

the potassium 

bichromate. 

The E. M. F. 

is about 2.14 

volts, and the 

cell is used for open-circuit or semirclosed circuit work. Another 

form of the Fuller type is shown in Fig. 48. 

51. Partz Acid Gravity Cell. — In the Partz acid gravity 
form of cell (Fig. 49) the electrolyte which surrounds the 



Fig. 47. — Fuller Cell. 

Zinc in dilute H2SO4 in porous cup, carbon 
in bichromate solution. 




Fig. 48. — Fuller Cell. 

Zinc in porous cup with mercury and dilute H2SO4 
bichromate solution. 



carbon in 



PRIMARY CELLS 



45 




Fig. 49. — Partz 
Cell. 



zinc is either magnesium sulphate or common salt. The 
depolarizer is a bichromate solution which surrounds the 
perforated carbon plate located in the bottom of the jar. A 
vertical carbon rod fits snugly into the tapered hole in the 
carbon plate and extends through the cover forming the posi- 
tive pole. The depolarizer, being heavier than the electrolyte, 
remains at the bottom of the jar, and the two hquids are thus 
kept separate. This depolarizer is placed on 
the market in the form of crystals, known as 
sulpho-chromic salt, made by the action of sul- 
phuric acid upon chromic acid. When dis- 
solved, its action is similar to that of the 
chromic acid solution. After the cell has been 
set up with everything else in place the crystals 
are introduced into the solution, near the bot- 
tom of the jar, through the vertical glass tube 
shown, and slowly dissolve and diffuse over the 
surface of the carbon plate. When the cur- 
rent weakens, a few tablespoonfuls of the salt introduced 
through the tube will restore the current to its normal value. 
The cell should remain undisturbed to prevent the solution 
from mixing. Its E. M. F. is from 1.9 to 2 volts, and the 
6 in. X 8 in. size has an internal resistance 
of about 0.5 ohm. Since the depolariza- 
tion is quite effective, the cell may be used 
on open- or closed-circuit work. 

52. Bunsen and Grove Cells. — The 
Bunsen and Grove cells are of the two-fluid 
type, the solutions being separated by a 
porous partition. The Bunsen cell (Fig. 50) 
has a bar of carbon immersed in strong 
nitric acid contained in a porous cup. 

^. f,^ -o This cup is then placed in another vessel 

Cell. containing dilute sulphuric acid, and im- 

Carbon in porous cup with mersed in the same liquid is a hollow^ 
HNOa. zinc in dilute H.S0. cylindrical plate of ziuc, which nearly sur- 
rounds the porous cup. The hydrogen, starting at the zinc, 
passes through the porous partition, and immediately enters 
into chemical action with the nitric acid, so that none of it 



Carbon^ 




46 LESSONS IN PRACTICAL ELECTRICITY 

reaches the carbon. There are produced by this action water, 
which in time dilutes the acid, and orange-colored poisonous 
fumes of nitric oxide, which rise from the cell. If the nitric acid 
first be saturated with nitrate of ammonia, the acid will last 
longer and the fumes will be avoided. Strong sulphuric acid 
cannot be used in any battery; generally 12 parts by weight, 
or 20 by volume, of water are mixed with one part of sulphuric 
acid. 

Grove used a strip of -platinum instead of carbon in his cell. 
A solution of bichromate of potassium (as in ^ 49) is frequently 
substituted for the nitric acid in the porous cup, thereby avoid- 
ing disagreeable fumes. The Bunsen and Grove cells produce 
powerful and constant currents, and are well adapted for ex- 
perimentation, but they require frequent attention, and are 
expensive, so that they are httle used for work of long dura- 
tion. The E. M. F. of these cells is from 1.75 to 1.95 volts. 

53. Daniell CeU. — The Daniell cell is made in many forms 
and is called by various names, such as Gravity cell (Fig. 51), 
Bluestone cell. Crowfoot cell, etc. It is a 
closed-circuit cell and is much used in 
practice for giving constant currents of 
long duration. Zinc and copper elements 
are used. 

An explanation of the theory of a 
simple form, Fig. 52, will answer for all 
forms of this class; the elements are sepa- 
rated by a thin partition of unglazed pot- 
tery. On the zinc side of the partition is 
^'DfiielTceir^^ put dilute sulphuric acid (H2SO4), or 
simply water if the cell is not required for 
immediate use; on the copper side is placed sulphate of copper 
(CUSO4) dissolved in water, together with some sulphate of 
copper crystals (bluestone) to maintain the supply of copper 
sulphate solution. When the circuit is closed, as shown at the 
right, the zinc combines with the (SO 4) of the sulphuric acid, 
forming sulphate of zinc (ZnS04), and thus sets free the two 
atoms of hydrogen (H2). 

This hydrogen gas passes through the porous partition, 
but instead of collecting on the sides of the copper plate, it 




PRIMARY CELLS 



47 



meets with the sulphate of copper (CUSO4), and having a 
greater natural affinity for the (SO 4) than the copper (Cu) 



balvanomefer 




[Sulphate \ 
\of Copper j 



V,V<\//,'<'//<'/J 



Fig. 52. — Chemical Action in the Daniell Cell. 

possesses, it displaces the copper and forms sulphuric acid 
(H2SO4), setting free pure metallic copper, which is deposited 
upon the copper plate. This continuous extraction of metal- 
lic copper from the solution would soon 
weaken it, were it not for the fact that 
the copper crystals dissolve and thus 
automatically keep the solution saturated. 
To maintain a constant current for an 
indefinite time, therefore, it is only neces- 
sary to keep up the supply of copper 
crystals and zinc. The cell has an E. 
M. F. of about one volt and gives a 
small but steady current. 

A student's small Daniell cell is shown in Fig. 
53. It is of the double-fluid type. A rod of 
weU-amalgamated zinc is immersed in -a solution 
of dilute sulphuric acid contained in the porous 
cup. The porous cup is placed in a glass jar con- 
taining a saturated solution of copper sulphate 
and a copper electrode that surrounds the porous 
cup. After a time it is necessary to replenish the 
copper sulphate, as it becomes weak, due to the 
metallic copper having been taken from it. The sulphuric acid also changes 
to zinc sulphate. Zinc sulphate is sometimes used instead of sulphuric 
acid, as it reduces the wasteful consumption of the zinc, but it should be 
pure. 




Fig. 53. — Student's 
Porous-Cup Daniell Cell, 



48 



LESSONS IN PRACTICAL ELECTRICITY 



The cell gives a constant potential of about 1.1 volts, the current on short- 
circuit is small, but since polarization is eliminated it is a good cell to 
use for electrical measurements where a constant source of E. M. F. is 
required; see Lesson XIX. 

54. Leclanche Cell. — The Leclanche cell is an example of 
the single solution type, and utilizes a soHd depolarizer sur- 
rounding the negative element, which is generally carbon, the 
positive element being zinc. The hquid used is a strong solu- 
tion of ammonium chloride, commonly known as sal-ammoniac, 
and much resembles table salt. In the porous-cup type of cell, 

Fig. 54, a carbon slab C is placed in the 
porous cup P and surrounded by a mixture 
of small pieces of carbon and manganese 
dioxide, the top being covered by means of 
pitch, leaving one or two small holes for air 
and gas to pass through. The depolarizer 
will take care of a limited amount of the 
hydrogen produced when the cell is on closed 
circuit, but if the circuit be closed for any 
length of time polarization occurs. The cell 
Leclanche is thus of the open-circuit class, and will fur- 
nish a moderate current where it is required 
Zinc is dissolved only when the cell is 
being used. This type of cell is much used for gas lighting and 
bell work, and requires very Httle attention. Water must be 
added as the solution evaporates, and the zinc rod replenished 
when necessary. The E. M. F. is about 1.4 volts and the inter- 
nal resistance is about 4 ohms. 

Directions for Setting Up the Leclanche Cell. — 1. Place in the glass 
jar six ounces of ammonium chloride (sal-ammoniac), pour in water until 
the jar is one-third fuU, and stir thoroughly. 

2. Put in the porous cup and add water if necessary until the level of 
the water is within 1| inches of the top of the porous cup. 

3. Put the zinc in place and set the cell away, without connecting up, 
for ten or twelve hours, to allow the liquid to thoroughly soak into the 
porous cup. Tliis action will lower the level of the Hquid to about two- 
thirds the height of the jar, at which level it should be kept, by adding 
water as it evaporates. The ceU is then ready for use. 

55. Gonda Leclanche Cell. — The Gonda cell is a modifica- 
tion of the porous-cup Leclanche cell, in which the manganese 




Fi2 



Cell, 
only intermittently. 



PRIMARY CELLS 



49 





has been mixed with some gelatinous binder and compressed 

into slabs, under hydrauhc pressure. Two such slabs or prisms, 

one on each side of the carbon plate, are held 

in position by rubber bands (Fig. 55). A zinc 

rod and a sal-ammoniac solution are used. 

This cell was designed to dispense with the 

porous cup. 

56. Carbon Cylinder Cell. — Carbon pos- 
sesses a natural power to prevent a limited 
amount of polarization by absorbing the hy- 
drogen gas coming from the zinc rod, so that 
we find it used in a variety of shapes for open- 
circuit cells under a variety of names, such as 

Samson, Hercules, Law, 

National, Standard, etc. 

In all these types of cells Fig- 55. — Gonda. 
1 • J • Leclanche Elements, 

sal-ammoniac and zmc 

are used, and by corrugating the carbon, 
fluting it, or making concentric cylinders, 
special merits are claimed in each case. 
Fig. 56 illustrates a 
carbon cyhnder cell; 
sometimes the cylin- 
der is moulded from 
a mixture of carbon 
and manganese di- 
oxide. The Samson 

cell has its carbon made in the form of a 

porous cup which is filled with oxide of 

manganese to prevent polarization. Still 

another form of the same make is shown in 

Fig. 57, in which the space between the 

two concentric carbon cylinders has been 

filled with oxide of manganese and then 

sealed in. The zinc rod is prevented from 

touching the carbon by means of a porcelain insulator. About 

4 to 6 ounces of sal-ammoniac are generally used for cells of 

ordinary size. The salt is placed in the jar, water is poured in 

until it is about two-thirds full, and then stirred till all the salt 



Fig. 56. — Carbon 
Cylinder Cell. 




Fig. 57. — Section 
through Carbon Cyl- 
inder Showing MnOa 
Depolarizer. 



50 



LESSONS IN PRACTICAL ELECTRICITY 



Amalgamated 
Zinc Plates 



is dissolved. When the carbon cyhnder .is inserted the solu- 
tion should be within \\ inches of the top of the jar. These 
cells should not be put in warm places, as over the heater in 
a cellar, on account of the rapid evaporation of the electrolyte. 
The E. M. F. is from 1.4 to 1.6 volts for the different forms of 
this type of cell. 

57. Edison-Lalande CelL — The Edison-Lalande type of 
cell is a single-fluid cell with a solid depolarizer, but is ad- 
mirably adapted for use on 
closed-circuit work, as for small 
motors, electrotyping, teleg- 
raphy, etc. Zinc is the posi- 
tive, and black oxide of copper 
(CuO) the negative, element. 
The exciting liquid is a solution 
of caustic potash. The oxide 
of copper is obtained by the 
process of roasting copper 
turnings, thereafter ground 
into a fine powder and com- 
pressed into solid blocks, from 
which plates of a suitable size 
are cut. 

These plates are suspended 
from the cover of the battery 

Zinc and copper oxide in caustic potash jar (Fm. 58) bv a liffht frame- 
solution. 1 ? J r.i, 

work 01 copper, one end of the 
frame-work terminating as the positive pole of the battery. On 
each side of the copper oxide element is suspended a zinc plate, 
which is prevented from coming into contact with the copper 
oxide plate by means of vulcanite buttons. When the circuit 
is closed the electrolyte, caustic potash (KOH), is decomposed, 
the oxygen forming, with the zinc, oxide of zinc, which in turn 
combines with the electrolyte to form a double salt of zinc and 
potassium known as potassium zincate (K2Zn02). The potas- 
sium liberated by the decomposition of the electrolyte reduces 
the copper oxide to metalHc copper and also forms caustic pot- 
ash, thus keeping the solution of the same strength. It is im- 
portant to see that the oxide plates are entirely submerged in 




^ Plate of Com pressed Oxide Copper 

Fig. 58. — Edison-Lalande Cell. 



PRIMARY CELLS 



51 




the caustic potash solution. Heavy paraffin oil is poured on 

top of the solution, so as to form a layer about one quarter inch 

deep on the surface, to prevent evaporation. When oil is not 

used creeping salts are formed and 

the life of the battery is reduced 

fully two-thirds. The E. M. F. is 

low, only 0.7 of a volt, but the 

internal resistance is also very low, 

so that quite a large current can 

be drawn from the cell. 

58. Weston Standard Cell. — A 
standard cell is one which is capable 
of maintaining a constant E. M. 
F. for a considerable time on open 
circuit, and in consequence such 
cells are used as standards of 
potential differ- 
ence in electrical 
measurements. Fig. 59. 
The Weston stand- 
ard cell uses mercury as the positive electrode 
and an amalgam of 12 per cent cadmium as the 
negative, and the electrolyte is cadmium sul- 
phate. It produces a P.D. of 1.0183 volts at 
20° C. A standard cell is not intended to 
deliver current, in fact high resistances are 
used with it so that the current drawn from 
the cell shall be infinitesimal. 

59. Dry Cells. — Dry cells differ from those 
already described in that the exciting fluid is 
Fig. 60. — Dry combined with some special absorbent, such as 
Cell, External sawdust, etc., or is made into a jelly. In the 
^^^^' usual type of dry cell the zinc element is in the 

form of a cylindrical container, which holds the other element 
(carbon), the depolarizer (manganese dioxide), and the exciting 
mixture. In one type the mixture or electrolyte has the fol- 
lowing proportions by weight: oxide of zinc, 1 part; sal-am- 
moniac, 1 part; chloride of zinc, 1 part; water, 2 parts. The 
chemical reactions in this cell are the same as those of the 






•^I^Y CEt*' 



^Q^KNlft^^ 



\'- Waterproof 
Cement 
■Fine Sand 

■Ground Carbon 
and Manganese ^ 
Peroxide Moistened 
wifhSalamoniac 
and Zins Chloride 
Solution. 

^-Zinc Cylinder 
'^Cardboard Cover 



BloffingPaper 
L ining. Safurafed 
wiih Salamoniac 
and Zinc Chloride 
Solution. 



Dry Cell, Sectional 
View. 




52 LESSONS IN PRACTICAL ELECTRICITY • 

Leclanche cell, If 54. Fig. 59 shows the internal construction of 
a dry cell and Fig. 60 shows the cell complete. Dry cells, being 
portable, are very convenient for use where only an intermittent 
current is required. The E. M. F. is about 1.4 to 1.6 volts. 
The most common standard size of dry cell is 2| inches in di- 
ameter and 6 inches high, known as No. 6, but many smaller 
sizes down to j% X IJ inches aj:e made for use in pocket flash- 
lights. 

60. Classification of Primary Cells. — 

Classified by f Open-circuit cells (Grenet, Lelanche). 

polarization \ Closed-circuit cells (Daniell, Lalande, Fuller). 
„, -fi pi u f Single-fluid cells (Grenet, Lelanche, Lalande). 
Ciassitied by , double-fluid cefls (Bunsen, Grove, Daniell, 

construction | jr^ner). 

f Liquid depolarizer (Grenet). 
Single-fluid cells with \ Solid depolarizer (Leclanche, La- 
[ lande) . 

61. Chemicals for Cells and Some Chemical Sjrmbols. — 
Copper Sulphate (blue vitriol), CUSO4 

Zinc Sulphate (white vitriol), ZnS04 
Ammonium Chloride (sal-ammoniac), NH4CI 
Bichromate of Soda, Na2Cr207 
Bichromate of Potassium, K2Cr207 
Chromic Acid, CrOa Lead Peroxide, Pb02 

Caustic Potash, KOH Sulphuric Acid, H2SO4 

Caustic Soda, NaOH Nitric Acid, HNO3 

Copper Oxide, CuO Hydrochloric Acid, HCl 

Manganese Dioxide, Mn02 Silver Chloride, AgCl 

Lead Oxide, PbO Zinc Chloride, ZnCl2 



QUESTIONS 

1. Since the hydrogen gas is evolved from the zinc when it is placed 
in dilute acid, how do you account for the fact that in a voltaic cell, when 
connected to a circuit, the hydrogen gas is evolved at the copper plate, 
yet the copper is not attacked by the acid? 

2. Upon what does the E. M. F. of a cell depend? 

3. Would you expect a very large cell to have the same E. M. F. as 
a small one of the same kind made up in test tube? Why? 



PRIMARY CELLS 53 

4. Give a list of some materials used in cells, in the order of their 
potential difference in dilute sulphuric acid. 

5. A cell is composed of copper and iron in dilute sulphuric acid. 
Draw a sketch indicating the + and — plates and electrodes, and the direc- 
tion of current flow when the plates are connected. 

6. What is local action in a cell? How is it prevented? 

7. What is the distinction between open- and closed-circuit cells? 

8. Why are there so many different makes of cells on the market, 
and what is the general distinction between them? 

9. Describe a two-fluid cell. Give an example. 

10. What is a depolarizer? Give an example of a cell with a sohd 
and Uquid depolarizer, and state how the depolarizer acts in each. 

11. Describe the Daniell cell and explain the chemical action. 

12. Describe a bichromate cell of the Grenet type. 

13. How does the Fuller cell differ from the Grenet cell, since the 
chemicals and plates used are identical? 

14. Describe the Leclanche porous-cup type of cell. How is polariza- 
tion reduced in this cell? 

15. How does the Edison-Lalande cell differ from the Leclanche 
cell, since they both use sohd depolarizers? 

16. Which of the two cells mentioned in Question 15 would you use 
for a spark-igniter on a gas engine? 

17. Describe fully the action of the Edison-Lalande cell. 

18. Describe the construction of a dry cell. 

19. Form a table of all the cells you know of, giving the + and — plates, 
electrolyte used, depolarizers, name and type (open or closed circuit) in 
the different columns of the table. 



LESSON V 
RESISTANCE 

Resistance — The Unit of Resistance — Conductors and Insulators — 
Table III — Wire Measure — The Circular Mil — The Square 
Mil — Laws of Resistance — Calculation of Resistance — Table 
IV — Wire Calculations — Specific Resistance, Relative Resistance 
and Conductivity of Metals — Table V — The Wire Gage — 
Table VI — Internal Resistance of a Battery — Rheostats — Re- 
sistance of Connections — Laboratory Rheostats — Questions and 
Problems. 

62. Resistance. — All bodies offer some opposition to the 
passage of an electric current through them. Pipes offer 
opposition to the flow of water through them, due to the 
friction between the running water and the sides of the pipes. 

Electrical resistance is the opposition offered by any substance 
to the flow of an electric current through it. No conducting 
body possesses perfect conductivity, but every conductor offers 
some resistance to the passage of a current. All bodies con- 
duct differently, some offering more opposition to the flow of 
current than others. If the opposition is small, the con- 
ductivity is good, and the body is classed as a conductor. When 
the opposition (resistance) is high, the conductivity is poor, 
and the substance is classed as a poor conductor, which ranks 
it as a good insulator. The function of an insulator is to 
obstruct the flow of current. With a good conductor for 
conducting current, and a good insulator for confining it to 
the conductor, we have the practical conditions for handling 
electricity. The metals and alloys are good conductors. 

Resistance is the reciprocal of conductivity. The greater the 
conductivity of a body the less its resistance ; the one decreases 
in the same ratio as the other increases. 

63. The Unit of Resistance. — The unit of resistance is 
called the ohm, and is the resistance that would be offered to 

54 



RESISTANCE 55 

the flow of an unvarying electric current by a column of mer- 
cury 106.3 centimeters long, weighing 14.4521 grams and having 
a uniform cross-sectional area, at a temperature of 0° Centigrade 
(or 32° Fahrenheit). In practice the value of the ohm, corre- 
sponding to the above standard, is as follows, approximately: 

1 ohm = 1000 feet of copper wire xV i^ch diameter (No. 10 
B. & S.). 

1 ohm = 250 feet of copper wire aV inch diameter (No. 16 
B. &S.). 

1 ohm = 2 pounds of copper wire 2V inch diameter (No. 16 
B. & S.); there are 125 feet per pound. 

For wires of the same length the resistance depends upon 
the size of the wire, for example: 

1000 feet of copper wdre nearly ^ inch diameter (No. 0000 
B. & S.) = 0.04998 ohm. 

1000 feet of copper wire roVo inch diameter (No. 40 B. & S.) 
= 1070 ohms. 

In calculating or measuring very low resistances one mil- 
lionth of the value of an ohm is sometimes used and called 
the microhm. 

To express a resistance in microhms multiply its value in 
ohms by 1,000,000, or 

microhms = ohms X 1,000,000 (1). 

microhms 

"'^^ = 1:000:550 ®. 

In measuring very high resistances one million ohms are 
used as the unit and called a megohm (often abbreviated meg.). 

ohms 
megohms = ^^^^^^^^ • (3). 

ohms = megohms X 1,000,000 (4). 

Problem 1. — What is the equivalent resistance in megohms of 
47,500,000 ohms? 

T, r, ^ ro^ 47,500,000 ^^ ^ 

By Formula (3) 1 000 000 " megohms. 

Problem 2. — Give the equivalent resistance in microhms of 0.00385 
ohm. 

By Formula (1) 0.00385 x 1,000,000 = 3850 microhms. 



56 



LESSONS IN PRACTICAL ELECTRICITY 



. / 



Problem 3. — What is the equivalent resistance in ohms of 225 mi 
crohms? i 

By Formula (2) ^^qqq^qqq = 0.000225 ohm. ' 

64. Conductors and Insulators. — In the following table the 
substances are arranged in the order of their conductance, the 
best conductors being at the top, and the best insulators at the 
bottom, of the list. Any substance in the table is approxi- 
mately a better conductor than any substance which follows 
it; thus, lead is a better conductor than mercury, but not so 
good as zinc, A slight variation in the quality of a substance 
would change its position in the list with reference to some 
other substance; for example, some marble is useless for switch- 
boards on account of metallic veins nmning through it. The 
same is true of slate, so that the position of these substances 
on the list is approximate. 

Table III. Conductors and Insulators 

Silver 
Copper 
Aluminum 
Zinc 

Brass (according to composition) 
Platinum 
Iron 
Nickel 
Tin 
Lead 

German silver (copper 2 parts, zinc 1, nickel 1) 
Platinoid (German silver 49 parts, tungsten 1) 
Antimony 
Mercury 
Bismuth 

Manganin (copper 14 parts, ferromanganese 5, nickel 1) 
Nichrome (nickel and chromium) 
' Charcoal and coke 
Carbon 
Plumbago 
Acid solutions 
Sea water 
Saline solutions 
Metallic ores 

Living vegetable substances 
Moist earth 



Good Conductors 
(metals and 
alloys) 



Fair Conductors < 



RESISTANCE 



57 



Partial Conduc- 
tors 



Nonconductors or 
Insulators 



Water 

The body 

Flame 

Linen and cotton 

Dry woods: mahogany, pine, rosewood, teak, etc. 

Marble 

Slate 

Oils 

Porcelain 

Dry leather and paper 

Wool and silk 

Sealing wax 

Sulphur and resin 

Gutta percha 

Shellac 

Ebonite 

Mica 

Paraffin wax 

Glass (varies with quaUty). 

Dry air. 




65. Wire Measure. — The Circular Mil. — In calculating 
the resistance of round wires for electrical purposes, a circular 
measure is used to express the cross- 
sectional area of the wire, since it is 
more convenient than the old method 
of measuring the area of circles in 
square inches; and a circular unit of 
area, the circular mil, is used instead 
of a square unit of area. One circu- 
lar mil is the area of a circle whose 
diameter is one mil. The term mil 
means one one-thousandth of an inch 
(toVo or 0.001 inch = 1 mil). 

If the diameter of a wire measures 2 mils (rwoo or 0.002 
inch), then it has a sectional area of 4 circular mils, the 
area being obtained by expressing the diameter of the wire in 
mils and squaring it (multiplying it by itself). The square 
of any diameter, expressed in thousandths of an inch, will 
give as a product the number of circular units that can be 
placed side by side in a square the sides of which are equal to 
the diameter that has been squared; the sum of the areas of 



Fig. 61. — Diagram Illus- 
trating Circular Mil Areas. 

Area of large circle equals the area 
of the nine small circles. 



58 LESSONS IN PRACTICAL ELECTRICITY 

the small circles contained within such a square equals the 
area of the large circle. This is illustrated in Fig. 61, where 
the area of the large circle equals the sum of the areas of the 
nine small circles. This is evident from the following: If we 
take the diameters of the small circles as unity, then the diam- 
eter of the large circle is three. The area of each of the small 

circles equals ^ = 0.7854 (that is V x 0.7854); the sum of the 

areas of the small circles equals 7.0686 (that is 9 x 0.7854) ; the 
area of the large circle equals 3^ x 0.7854 = 9 x 0.7854 = 7.0686. 
Therefore, since the area of the large circle equals the sum 
of the areas of the small circles, the area of a wire in circular 
mils is equal to the square of the diameter expressed in mils. 

First: To find the circular mil area of any round 

W^RE WHEN its DIAMETER IN INCHES IS KNOW^NI 

Express the diameter in mils and square it. 
Let d = diameter in mils, 

d^= diameter squared, 
C. M. = circular mil area. 



Then 



C.M.= d2 . (5). 

Problem 4. — What is the circular mil area of a wire j inch in diameter? 

250 
Since 1 inch = 1000 mils, I inch = — -— or 250 mils. 

1000 

By Formula (5) C. M. = d^ = d x d = 250 x 250 = 62,500 C. M. 

Second: To find the diameter of any wire w^hen 
the circular mil area is known: 

Extract the square root of the circular mil area. The result is 
the diameter expressed in mils, or 



d^VoM (6), 



Problem 5. — What is the diameter of a wire if the area is 6530 C. M. 
(No. 12 B. & S.)? - 

By Formula (6) d = V C. M. = V 6530 = 81 mils nearly, or 0.081 
inch diameter. 

66. The Square Mil. — Many electrical conductors, such as 
bus-bars, copper ribbon, etc., are square or rectangular in 



RESISTANCE 59 

cross-sectional area, and in computing areas of such conductors 
the square measure is used, for which the units are the square 
mil and the square inch, one square mil being the area of a 
square whose sides measure one mil or one one-thousandth of 
an inch. One square mil equals 0.000001 square inch. It is 
sometimes necessary to find the equivalent area in round wire 
measure of conductors of rectangular cross section; the rela- 
tions used in this connection are: one square mil equals 1.2732 
circular mils, and one circular mil equals 0.7854 square mil. 

Third: To find the area of a rectangular wire 

IN SQUARE mils: 

Express the dimensions in mils and find the product of the 
dimensions. The result is the area in square mils. 
Let c = thickness in mils, 

d = width in mils. 

Sq. mils = cxd (7). 

Problem 6. — A copper ribbon for a field coil measures f inch x | inch. 
Find its square mil area. 

I = 0.625 inch, or 625 mils; ^ = 0.125 inch, or 125 mils. 

By Formula (7) Sq. mils = c x d = 125 x 625 = 78,125 sq. mils. 

Fourth: To convert circular mil area into square 
mil area: 

Multiply the circular mil area by 0.7854- The result will be 
in square mils. 

Since one circular mil = 0.7854 square mil, therefore, 

sq. mils = C. M. X 0.7854 (8). 

Problem 7. — What is the square mil area of a wire | inch in diameter? 
In Problem 4 the area was calculated to be 62,500 G. M. 
By Formula (8) Sq. mH area = C. M. X 0.7854 = 62,500 X 0.7854 = 
49,087 sq. mils. 

Fifth: To convert square mil area into circular 
mil area : 

Multiply the square mil area hy 1.2732. The result will be 
in circular mils. 

Since one square mil = 1.2732 mils, it follows that 

C. M. = sq. mils X 1.2732 (9). 



60 LESSONS IN PRACTICAL ELECTRICITY 

Problem 8. — Find the circular mil area of the copper wire in Prob- 
lem 6. 

In Problem 6 the square mil area = 78,125. 

By Formula (9) C. M. = sq. mils x 1.2732= 78,125 x 1.2732 = 99,468 C. M. 

67. Laws of Resistance. — 

I. It is the cross-sectional area of a material which conducts 
and not its surface. This can be proved by using a wire tube 
in comparison with a sohd wire of the same outside diameter 
(Law I, Fig. 62). 

II. The resistance of a conductor is directly proportional to its 
length. Thus, 2000 feet of copper wire 0.1 inch diameter will 
have 2 ohms resistance; 10,000 feet, 10 ohms, etc. (Law II, 
Fig. 62). 

III. The resistance of a conductor is inversely proportional j 
to its cross-sectional area, and in the case of round wire inversely ! 
proportional to the square of the diameter. The area of a round i 
wire varies directly as the diameter squared, or area varies as d^. • 
A wire one half inch in diameter has four times as great a resis- 
tance as a wire one inch in diameter, because the area is one '■ 
quarter as large. Again: No. 24 (B. & S.) wire has a diameter : 
of 0.02 inch and No. 30 has a diameter of 0.01 inch, or one half ;; 
the diameter of No. 24; 38 feet of No. 24 have a resistance of \ 
one ohm, and 9.5 feet of No. 30 have a resistance of one ohm; < 

38 38 • 

this agrees with the foregoing statements since — = — = 9.5 \ 

(Law III, Fig. 62). _ I 

IV. The resistance of a conductor of given length and cross \ 
section depends upon the material of which it is made. For ■. 
example, the resistance of 1000 feet of copper wire to inch 
diameter (No. 10 B. & S.) is about 1 ohm, while the resistance i 
of a piece of iron wire of the same length and cross section j 
is about 6 ohms, and a similar piece of German silver about | 
12 ohms (Law IV, Fig. 62). \ 

V. The resistance of a conductor depends upon the temperature ' 
and is affected by any other cause which modifies its molecular i 
condition. If copper, German silver, and platinoid are heated i 
the resistance of the copper is increased nearly 10 times as j 
much as that of the German silver, and 20 times as much as j 
platinoid (Law V, Fig. 62 ). ! 



RESISTANCE 



61 



All metals have their resistance increased by an increase of 
temperature. Carbon and all electrolytic conductors {battery 



^1000 ft- 



' "y" WlllimillWUUUllil 



itiiiiiiiDiMm 



ml 



No. 10 B. & S. Copper Wire 



Resistance f-Ofim 



""^ Ol /JJf/JWWH-l/^hMU.'- .^^^Htt^W WHtift^ 






No. 10 B. & S. Copper Tubing Resistance l§-Olims 

LAW I 
^ 500 ft. >| 



Resistance j Qlim 



I'^^lllllllllllll: 



niiiiiiiiiinllliiniiiiniiiiiiUiilllW 



No. 10 B. £ S. Copper Wire 



Resistance f-Ohm 



\,lK\t^ Z 



SS" 



No. le B. &. S. Copper Wire 



Resistance 4-Ohms 



^Jr- ^lllliiiiiiiiinu 



iiiiiiliijiiiiiiiliiimlW)) 



No. 10 B.Su S. Copper Wire 



Resistance hOlim 



LAW 3 



"^m 



niiiiiiiiiiiiiiniimiiiiDm 



No. 10 B. '&. S. Copper Wire 



Resistance I- Ohm 






iiliiiiiiiiiiiiivmiM 



No./O-B.&S. Iron Wire 



Resistance 6. Otims 



LAW 4 



s§ 



mmuiuuimlwiim. 



niiiiDinutnimiumm 



Temperature 75 F. 



Resistance hOlim 



milllllllllllllllllllllllll//llli,n. 



Temperature 100° F. 



i'n/iiii/iji/i)/ii//iiiiiiiiiiiiiiiiiiiiiiiiiiji) 
Resistance. 1.0525 Otims 



m, lliiiiiiiiiiiiiiiiDinniii,,,,. 



■■"".nnllnin.n. ■ ■ ••nnnlllllUmlljjjm 

Temperature 50° F Resistance .9475 Ohms 

No. iO B.S.S. Copper Wire 
LAW 5 
Fig. 62. — Laws of Resistance for Electrical Conductors. 



solutions) decrease in resistance as the temperature increases. 
The resistance of copper increases about one quarter of one 
per cent (0.0023) for each degree temperature rise, Fahrenheit 



62 



LESSONS, IN PRACTICAL ELECTRICITY 



scale. See K 241. The hot resistance of the carbonized fila- 
ment of an incandescent lamp is about one half the cold re- 
sistance. The Mazda tungsten filament lamp is just the 
opposite; its filament has a higher resistance while incan- 
descent than when cold. 

The following experiments will verify the above laws. The 
resistances used in these experiments consists of four spools of 
wire, as follows: spool No. 1 contains 25 feet of No. 24 B. & S. 
copper wire, diameter 20.1 mils; spool No. 2, 50 feet of No. 24 




Daniell Cell Detector Galvanometer Resistance Spool Set 
Fig. 63. — Connections of Apparatus for Verifying Laws of Resistance. 

(See Experiments 23 to 27). 

B. & S. copper wire; spool No. 3, 25 feet of No. 18 B. & S. 
copper wire, diameter 40.3 mils; spool No. 4, 25 feet of No. 24 
B. & S. German silver wire. 

Experiment 23. — Connect spool No. 1, of the resistance spool set, to a 
Student's Daniell cell, with the detector galvanometer (Fig. 172) in the 
circuit, as shown in Fig. 63, and note deflection of the needle. 

Experiment 24. — Connect spool No. 2 in place of No. 1, and note that 
the deflection is smaller than before. Why? (Law II.) 

Experiment 25. — Connect spool No. 3 in place of No. 2, and note 
deflection. It is greater than was obtained with either Nos. 1 or 2. Why is 
this so, since its wire is of the same length and material as No. 1 ? (Law III . ) 

Experiment 26. — Substitute spool No. 4 for No. 3; note deflection. 
This deflection is smaller than in any of the other cases. The wire on 
spool No. 4 is of exactly the same length and cross-sectional area as that 
on spool No. 1. Why is the deflection so much smaller? (Law IV.) 

Experiment 27. — Connect several bichromate cells in series and to 
spool No. 4, passing a current through it for a short time , The spool be- 



RESISTANCE 63 

comes warm. Now connect it again in the same circuit as in Experiment 
26, and note that the deflection is smaller than before. Why is this so, 
since it is exactly the same spool as was used in Experiment 26? (Law V.) 

68. Calculation of Resistance. — In calculating the resis- 
tance of metal conductors, the resistance of a mil-foot of the 
metal is taken as a constant (K), and used in computing the 
resistance of a wire of correspondingly greater length and area 
than the mil-foot. The mil-foot is used as a unit wire having 
a cross-sectional area of one circular mil and measuring one 
foot in length. The resistance per mil-foot (K) is sometimes 
called- the resistivity or specific resistance of a material, and varies 
with different materials. See If 70. 

One foot of copper wire rsVo inch in diameter has a resis- 
tance of 10.79 ohms (K) at 75° Fahrenheit. Ten feet will have 
107.9 ohms. One foot of copper wire roVo inch in diameter 
will have one fourth the resistance or 10,79 divided by 4 = 2.69 
ohms. If this last wire were iron, it would have 6 times the 
resistance, or 16.14 ohms. Resistance varies directly as the length, 
inversely as the cross-sectional area, and with the material of the 
conductor. 

Given the length and area of any wire to find its 
resistance i 

The resistance of any wire is equal to its length in feet 7nuUi- 
plied by the resistance of a mil-foot (K) and this product divided 
by its area in circular mils. 

Let L = length of the wire in feet, 
R = resistance in ohms, 
C. M.= circular mil area, 

K = resistance of one mil-foot in ohms. 

^'^^"' ^^irw. ('°)- 

Problem 9. — Find the resistance of 1000 feet of copper wire having 

a cross-sectional area of 10,000 C. M. 

Since K for copper = 10.79, L =1000feet, CM. = 10,000, it follows from 

t? 1 /1A^^l,^-D KxL 10.79x1000 , ^__ , 

Formula (10) that R = ^ ,, = = 1.079 ohms. 

CM. 10,000 

The value of K is constant for the same wire, but different 
for each metal, and for copper at 75° Fahrenheit it is 10.79 ohms. 



64 LESSONS IN PRACTICAL ELECTRICITY j 

The value of K for other metals can be taken from the table 1 

below, and the resistance of any wire can be calculated when j 

its dimensions are known. The resistance obtained corre- \ 

sponds with the temperature for which K is given. The follow- ; 

ing table gives the resistance of a foot of wire 0.001 inch in • 

diameter, or the values of K, for different metals when the i 

temperature is 68° Fahrenheit (see ^ 241). K therefore is \ 

the resistance of 1 mil-foot. ; 

Table IV. Resistances of a Mil-foot of Metals (Values of K) i 

Silver, 9.84 Zinc, 36.69 German silver, 128.29 j 

1 Copper, 10.79 Platinum, 59.02 ^platinoid, 188.93 

2 Aluminum, 17.21 Iron, 63.35 Mercury, 586.24 

Problem 10. — • Substitute an iron wire for the copper wire in Problem 9, I 
and find its resistance. 

By Formula (10) R = ||j^ = ^^f|jf^ = 6.335 ohms, \ 

where K for iron = 63.35. j 

Iron has thus about six times the resistance of copper. - j 

i 

69. Wire Calculations. — , 1 

Case 1. — Given the resistance and area of a wire \ 

TO FIND its length: I 

The length of any wire is equal to its resistance multiplied by { 

its circulo.r mil area, and this product divided by the resistance ] 

of a mil-foot (K) . ; 

J RxC.M. .... ; 

^:= ~~K - ^^^^- \ 

Problem 11. — What is the length of German silver wire wound on a i 

resistance spool, if its resistance is 500 ohms and the size of wire is No. i 

20 B. & S.? I 

No. 20 B. & S. = 1022 C. M. (from Table VI). K for German silver ! 

= 128.29 (from Table IV). I 

T, T. 1 /11^ T RxC.M. 500x1022^ ___„ , ^ ] 

By Formula (11) L = — = — tt^p^tt- = 3983 feet. ^ 

K 128.29 u j 

1 10.79, or (10.8) is generally used in practice as the value of K for- ; 
commercial copper at the average working temperature of 75° Fahrenheit. , 

2 Value for annealed aluminum (conductivity = 62 % that of copper). I 

3 German silver 49 parts, tungsten 1 part. I 



RESISTANCE 65 

Case 2. — Given the length and resistance of a wire 
TO find the area: 

The area in circular mils of any wire is equal to its length 
multiplied by the resistance of a mil-foot (K) and this product 
divided by its resistance. 

C. M. = ^^ (12). 

Problem 12. — What is the circular mil area of 1000 feet of a certain 
iron wire, if its resistance is 30 ohms? 

K for iron = 63.35 from Table IV. 

r» 1? 1 MON r^ A/r LxK 1000x63.35 om^r^A/r 

By Formula (12) C. M. = — - — = = 2111.6 C. M. 

R 30 

Case 3. — Given the area of a wire to find the 

weight. 

The weight per mile (5280 feet) of any bare copper wire in 
pounds is equal to the area in circular mils divided by the constant 
62.5. Copper weighs about 555 pounds per cubic foot; iron 
weighs about 480 pounds per cubic foot. 

Pounds per mile (bare copper wire) = ^^ ' (13). 

Pounds per foot (bare copper wire) = ^^r-y^ — ^^r— - . . (14). 
Pounds per mile (bare iron wire) =^ ^' ' (15). 

I Zi. lo 

Problem 13.— The circular mil area of a No. 10 B. & S. wire is 10,380. 
How many pounds of bare copper wire will be required for two lines run- 
ning a distance of 5 miles? 

By Formula (13) lbs. per mile = -^ — ~ = — ^ = 166.08 lbs. per mile. 

V y F g2.5 62.5 

Therefore the total weight is 166.08 x 5 x 2 = 1660.8 lbs. 

70. Specific Resistance, Relative Resistance and Conduc- 
tivity of Metals. — In comparing different materials, some 
standard of unit dimensions must be adopted. The com- 
mercial copper wire standard generally used is the Annealed 
Copper Standard (page 67), recommended by the United 
States Bureau of Standards, having a specific resistance 



66 



LESSONS IN PRACTICAL ELECTRICITY 



of 1.7241 microhms per cubic centimeter at a temperature of 
20° Centigrade. In scientific writings, specific resistance is 
usually given as the resistance between two opposite faces of 
a cube of the material at 0° Centigrade, instead of on the basis 
of a wire one foot long and one mil in diameter, which is gener- 
ally used in practice. The following table (Table V) gives the 
specific resistance for a centimeter cube and an inch cube of 
the materials, also the relative resistance and conductivity. 
Silver, the best conductor, has a conductivity of 100 %. 



Table V. Specific Resistance, Relative Resistance, and Conductivity 

of Conductors 





Resistance 


n INIicrohms 








at 0° Centigrade 






Metals 






Relative 
Resistance 










Conductivity 




Centimeter 


Inch 








Cube 


Cube 






Silver (annealed) 


1.521 


0.598 


l.OCO 


100 


Copper (annealed) 


1.639 


0.645 


1.075 


93 


Copper (hard drawn) 


1.670 


0.667 


1.096 


91 


Aluminum (annealed) .... 


2.76 


1.186 


1.81 


55 


Zinc 


5.87 


2.310 


3.86 


26 


Platinum 


9.04 


3.555 


5.93 


16.8 


Iron 


9.70 


3.814 


6.37 


15.7 


Lead 


19.60 


7.706 


12.90 


7.7 


German silver 


20.65 


8.127 


13.6 


7.4 


Mercury 


«6.14 


37.825 


63.2 


1.6 



71. The Wire Gage. — A number of wire gages, differing 
slightly from each other, have been originated by different 
manufacturers of wire, but the one generally used in this 
country is the B. & S. gage (Brown & Sharpe Manufac- 
turing Co.), commonly called the American Gage. Tables of 
several other gages will be found in the Appendix. Table VI 
gives the B. & S. gage. The first column gives the gage 
number; for example, the scale in the B. & S. gage is from 
No. 0000 (four naughts) wire (460 mils diam.) to No. 40 (3 mils 
diam.), the sizes decreasing as the gage numbers increase. The 
diameter, area, weight, length, and resistance are also given 
for each size wire. 



RESISTANCE 



67 



VI. "Wire Table, Standard Annealed Copper at a Temperature 
of 25° Centigrade (77° Fahrenheit) 







American 


Wire Gage 


(Brown & Sharpe) 




6 

CJ 

o 


Diam. 

in 
Mils 

d 


Area 


Weight 


Length 


Resistance 


Cir. Mils 

d2 


Lbs. pei 
1000 ft. 


Lbs. 
per ohm 


Feet 
per lb. 


Feet 
per ohm 


Ohms per 
1000 ft. 


Ohms 
per lb. 


0000 
000 
00 


460.0 
409.6 
364.8 


211660. 
167800. 
133100. 


640.5 
507.9 
402.8 


12810. 

8057. 
5067. 


1.561 

1.968 
2.482 


20010. 
15870. 
12580. 


1 0.04998 

1 .06303 

.07947 


0.00007805 
.0001217 
.0001935 




1 

2 


324.9 
289.3 
257.6 


105500. 
83690. 
66370. 


319.5 
253.3 
200.9 


3187. 
2004. 
1260. 


3.130 
3.947 
4.977 


9979. 

7913. 
6276. 


.1002 
.1264 
.1594 


.0003138 
.0004990 
.0007934 


3 

4 
5 


229.4 
204.3 
181.9 


52640. 
41740. 
33100. 


159. 3 
126.4 
100.2 


792.7 
498.6 
313.5 


6.276 
7.914 
9.980 


4977. 
3947. 
31.30. 


.2009 
.2534 
.3195 


.001262 
.002006 
.003189 


6 

7 
8 


162.0 
144.3 
128.5 


26250. 
20820. 
16510. 


79.46 
63.02 
49.98 


197.2 
124.0 
77.99 


12.58 
15.87 
20.01 


2482. 
1968. 
1561. 


.4029 
.5080 
.6400 


.005071 
.008064 
.01282 


9 
10 
11 


114.4 
101.9 
90.74 


13090. 
10380. 
8234. 


39.63 
31.43 
24.92 


49.05 

30.85 
19.40 


25.23 
31.82 
40.12 


1238. 
981.8 
778.5 


.8078 
1.019 
1.284 


.02039 
.03242 
.05155 


12 
13 
14 


80.81 
71.96 
64.08 


6530. 
5178. 
4107. 


19.77 
15.68 
12.43 


12.20 
7.673 
4.826 


50.59 
63.80 
80.44 


617.4 
489.6 
388.3 


1.620 
2.042 
2.570 


.08196 

.1303 

.2072 


15 
16 

17 


57.07 
50.82 
45.26 


3257. 
2583. 
2048. 


9.858 
7.818 
6.200 


3.035 
1.909 
1.200 


101.4 

127.9 
161.3 


307.9 
241.2 
193.7 


3.248 
4.095 
5.161 


.3295 
.5239 
.8330 


18 
19 
20 


40.30 
35.89 
31.96 


1624. 
1288. 
1022. 


4.917 
3.899 
3.092 


0.7549 

.4748 
.2986 


203.4 
253.5 
323.4 


153.6 
121.8 
96.59 


6.512 
8.210 
10.35 


1.325 
2.100 
3.349 


21 

22 
23 


28.46 
25.35 
22.57 


810.1 
642.4 
509.5 


2.452 
1.945 
1.542 


.1878 
.1181 
.07427 


407.8 
514.2 
648.4 


76.60 
60.74 

48.17 


13.06 
16.40 
20. 70 


5.325 
8.467 
13.46 


24 
25 
26 


20.10 
17.90 
15.94 


404.0 
320.4 
2.54.1 


1.223 
0.9699 
.7692 


.01671 
.02938 
.01847 


817.7 
1031. 
1300. 


38.20 
30.30 
24.02 


26.18 
33.01 
41.62 


21.41 
34.04 
54.13 


27 
28 
29 


14.20 
12.64 
11.26 


201.5 
159.8 
126.7 


.6100 
.4837 
.3336 


.01162 

.007307 
.004595 


1639. 
2007. 
2007. 


19.05 
15.11 
11.98 


52.43 
66.18 
83.40 


86.07 
130.8 
217.6 


30 
31 
32 


10.03 
8.928 
7.950 


ICO. 5 

79.70 
63.21 


.3042 
.2413 
.1913 


.002890 
.001818 
.001143 


3287. 
4145. 
5227. 


9.503 
7.536 
5.976 


105.2 
132.7 
167.3 


346.0 
550.2 
874.8 


- 33 
24 
35 


7.080 
6.335 
5.015 


50.13 
39.75 
31.52 


.1517 
.1203 
.09542 


.0007189 
.0004521 
.0002843 


6591. 
8310. 
10480. 


4.739 
3.759 
2.981 


211.0 
266.1 
335.5 


1391. 

2212. 
3517. 


36 

37 
38 


5.000 
4.453 
3.965 


25.00 
19.83 
15.72 


.07568 
.06001 
.04759 


.0001788 
.0001125 
.00007074 


13210. 
18660. 
21010. 


2.364 

1.874 
1.487 


423.0 
533.5 
672.7 


5592. 
8892. 
14140. 


39 
40 


3.531 
3.145 


12.47 

9.888 


.03774 
.02993 


.0C004448 
.00002798 


26500. 
33410. 


1.179 
0.9349 


848.2 
1070. 


22480. 
35740. 



68 



LESSONS IN PRACTICAL ELECTRICITY 



The fundamental resistivity used in calculating this table is the Annealed 
Copper Standard of the United States " Bureau of Standards," and is 
0.15328 ohm (meter, gram) at 20° Centigrade. The temperature coef- 
ficient for this particular resistivity is at 20° Centigrade = 0.00393, or 
at 0° = 0.00427. Specific Gravity = 8.89. 

This table is intended as an ultimate reference 
table and is computed to a greater precision than 
is desired in practice. 

72. Internal Resistance of a Battery. — 

Resistance in a voltaic circuit may be 
divided into two parts: internal resistance 
(r), which the current encounters in pass- 
ing through the liquid from one plate to 
the other, and external resistance (R), or 
that of the outer circuit (see Fig. 64). 
The current that a cell will give, therefore, 
depends upon its internal resistance, and 
will be greater the less this resistance, 
and vice versa. The internal resistance is 
governed by the same laws as the external 




Fig. 64. — The In- 
ternal and External 
Resistance of a Cell. 



resistance. Thus: 
r (internal resistance) 



Kx 



distance between plates 



areas of plates submerged 
or the internal resistance varies with 

(1) electrolyte used, 

(2) distance between the plates, 

(3) size or area of the plates. 

A battery to have a low internal resistance should have 
large plates placed near to each other. 

73. Rheostats. — The usual method of regulating and con- 
trolling the current required for various electrical purposes 
is by inserting, or taking out of a circuit, resistance. An 
adjustable resistance or any apparatus for changing the re- 
sistance without opening the circuit is called a rheostat. The 
function of a rheostat is to absorb electrical energy, and this 
energy, which appears as heat, is wasted instead of performing 
any useful work. A rheostat may be constructed of coils 
of iron wire, iron plates or strips; of carbon, either pulverized 
in tubes or in the form of solid rods or disks; German silver, 



RESISTANCE 



69 




Fig. 65. — One Type of Rheostat. 

Ward-Leonard starting box for starting 
motors. 



platinoid, or wires of other alloys wound on spools; columns of 
liquids, as water and mercury, etc. The cross-sectional area of 
the material must be sufficient 
to carry the current without ex- 
cessive heating. In rheostats 
used for regulating the current 
in commercial electric circuits 
no great degree of accuracy of 
the resistance coils is required, 
as is the case in laboratory rheo- 
stats ffl 75). 

Fig. 65 illustrates a commer- 
cial type of rheostat, in which 
the various coils are connected 
to brass buttons or contact seg- 
ments. By moving a metallic 
connecting arm over the seg- 
ments the coils are thrown in 
or out of circuit, and the re- 
sistance thus readily varied. The general plan of connections 

of a rheostat is shown in Fig. 66; 
the resistance can be adjusted from 
to 50 ohms in steps of 5 ohms. 
In some types of rheostats the wire 
is wound on an iron framework 
which has been previously dipped 
into a fireproof insulating enamel. 
The advantage of this construction 
is that the heat from the wire is 
dissipated much more rapidly, so 
that a much smaller wire can be 
used to carry a given current. The 
size of such an enameled rheostat, 
required for absorbing a given 
amount of energy, is much smal- 
ler than one made of coils of wire 
stretched in air on an iron supporting framework. 

74. Resistance of Connections. — When two surfaces are 
pressed lightly together the resistance of the contact is much 




Fig. 66. — Connections of a 
Rheostat. 



70 



LESSONS IN PRACTICAL ELECTRICITY 




Fig. 67. — Laboratory Type of Rheostat. 



greater than if the surfaces of contact slyb firmly pressed together. 

For tills reason all 
binding screw con- 
tacts should be 
thoroughly cleaned 
to a bright me- 
tallic lustre when 
used, and screwed 
down so as to clasp 
the wires firmly. 
All joints in elec- 
trical conducting 
systems should be 
soldered to decrease the resistance of contact. 

75. Laboratory Rheostats. — For making electrical measure- 
ments accurately standardized resistance boxes are required. 
The current passed through these rheostats is generally very 
small so that the resistance wire, generally an alloy such as 
German silver, platinoid, or manganin, is small in size and is 
wound on spools which are contained 
in a case, as shown in Fig. 67. Brass 
strips are mounted on the top of tKe 
case, and the terminals of each coil con- 
nected to two adjacent strips as shown 
in detail in Fig. 68. The insertion of a 
tapered metal plug into a tapered hole 
formed by the adjacent strips, short- 
circuits or cuts out the resistance coil. 
By removing the plugs, resistance is 
inserted in the circuit in which the box is connected. The 
resistance value of each coil is stamped on the box, as shown 
in Fig. 67, so that the resistance in circuit is found by the 
addition of the values of the coils unplugged. The coils are 
wound noninductively , ^ 260, and the size of the wire used 
must be such that no appreciable error will be introduced by 
the heating of the coils. 

QUESTIONS 

1. The conductivity of a porcelain rod is very low. 
affect its insulating quahties? 




^^ 



Fig. 68. — Connection 
of a Resistance Coil in 
Laboratory Rheostats. 



How will this 



RESISTANCE 71 

2. What is the function of an insulator? 

3. The resistance of 5 pounds of No. 36 platinoid wire is very high. 
How does this affect the conductivity? 

4. A battery sends a certain current through a piece of copper wire. 
Would the same cell send more or less current through another piece of 
copper wire twice as long but of double the area of the first piece? 

5. If the second wire in Question 4 was twice the length and twice 
the diameter of the first wire, what would be your answer? 

6. Current from a cell flowing through a piece of iron wire deflects 
a galvanometer needle 40 degrees. When a piece of aluminum of similar 
dimensions to that of the iron is substituted, the deflection is 55 degrees. 
How do you account for this, since both wires are exactly the same size? 

7. One mile of a certain iron wire has a resistance of 6 ohms. What 
will be the resistance of one-quarter of a mile of the same wire? 

8. What is the function of a rheostat? How is its resistance varied? 

9. What advantage does an enamel type of rheostat possess over one 
constructed in the form of coils? 

10. State what is meant by specific resistance? 

PROBLEMS 

1. The insulation of a wire measures 16.75 megs. What is its equiv- 
alent resistance in ohms? Ans. 16,750,000 ohms. 

2. What is the circular mil area of a wire fV inch in diameter ? Ans. 
35,156 CM. 

3. The circular mil area of a wire is 5625. What is its diameter ? 
Ans. 75 mils. 

4. An armature is wound with copper bars re by f of an inch. What 
is their equivalent area in circular mils? Ans. 89,522 C. M. 

5. The resistance of the series coil of a dynamo is 0.0065 ohm. Express 
its resistance in microhms. Ans. 6500 microhms. 

6. What is the square mil area of a No. 12 B. & S. copper wire ? Ans. 
5128 sq. mils. 

7. What is the resistance of 5 pounds of No. 18 B. & S. copper wire, 
allowing 5 per cent of its weight for insulation ? Ans. 6.251 ohms. 

8. The coils of a rheostat, constructed of No. 8 B. & S. iron wire, 
have a resistance of 10 ohms. What length of wire was required ? Ans. 
2608 feet. 

9. A rectangular wire has a square mil area of 20,616. What is 
the equivalent circular mil area ? ^Ans. 26,249 C. M. 

10. What size of B. & S. wire has an equivalent area to the wire in 
Problem 9 ? Ans. No. 6. 

11. Calculate the resistance of 2000 feet of No. 6 B. & S. copper wire. 
Ans. 0.822 ohms. 

12. Construct from your own calculations, a wire table for No. 12 
B. & S. copper wire, giving the circular mil area, square mil area, pounds 
per mile, pounds per foot, pounds per ohm, feet per pound, feet per ohm, 
ohms per pound, and ohms per foot. 



LESSON VI 
EFFECTS PRODUCED BY THE ELECTRIC CURRENT 

Effects of the Current — Heating Effect — Magnetic Effect — Chemical 
Effect — Electrolysis — Electrolysis of Copper Sulphate — Electrol- 
ysis of Zinc Sulphate — Electrolysis of Lead Acetate — Electroplat- 
ing — Electrotyping — Polarity Indicator — Questions. 

76. Effects of the Current. — A current of electricity is 
believed to be a transfer of electrons through a circuit, U 25; 
and since these carriers are so minute, a direct measurement of 
them is impractical. Consequently, an electric current is meas- 
ured by the effects it produces, all of which are commercially utilized. 
The effects manifested by a current of electricity are: Heating 
Effect, Magnetic Effect, Chemical Effect, and Physiological Effect. 
The first three of these effects are treated in this book. A cur- 
rent passed through the body produces muscular contractions, 
which are said to be due to the physiological effect. Electro- 
therapeutics deals with the study of this effect. 

By a direct or continuous current is meant one which flows 
always in the same direction, as, for example, the current from 
a battery or direct-current generator. In a pulsating current 
the direction is uniform, but the current strength varies. Most 
direct-current generators furnish a pulsating current, but the 
pulsations are so small that the current becomes practically con- 
stant. In an alternating current the direction is reversed at 
short intervals, and the current strength also varies periodically. ^ 
Such currents are furnished by alternating-current generators, 
usually called alternators. 

77. Heating Effect. — 

Experiment 28. — Connect the- terminals of a bichromate cell to a piece 
of No. 32 iron wire about one inch long. The wire becomes so hot that 
it is luminous, thus illustrating the heating effect of a current of electricity. 

^ In most of the following pages the references to current strength are 
true for direct currents, and exceptions must be made if other currents 
are considered. 

72 



EFFECTS PRODUCED BY THE ELECTRIC CURRENT 73 

The chemical energy inside of the cell is thus converted into electrical 
energy outside of the cell in the form of heat and light. If the .current 
is strong enough the wire will be melted. 

Experiment 29. — Substitute for the iron wire in Experiment 28 a piece 
of copper wire of the'same size and length. A smaller change of tempera- 
ture will be noted. 

Experiment 30. — Close the circuit of the cell without any fine wire 
in the circuit. More heat is now generated inside of the cell than in the 
external conducting wires. 

Every wire which conducts a current of electricity becomes 
heated to some extent as a result of the current, because the 
best conductors offer some opposition (resistance) to the flow 
of the current, and it is in overcoming this resistance that the 
heat is developed. If the wire is large in cross-sectional area 
and the current small, the heat developed will be so small 
in amount as not to be recog- 
nized by the touch, yet, never- •'^"'^'nhimenf 
theless, some heat is evolved /S^^iS^ . 
from the wire; upon the other i:ji;jpi'il!l!;i!ii^i^ ^ ' - 
hand, with a small wire and a \|!'^v_y^ '^°"mrts^^ 
large current it becomes quite ^^^^^^^'"'^^^^^ohss Buib 
hot. As the heat increases with 

the resistance of the conductor ^'^- ^^' " Electric Incandescent 

, j^amp. 

used, by employmg a poor con- 
ductor we obtain both hght and heat. This principle is used 
in the incandescent electric lamp, in which a high-resistance 
solid conductor called the filament is inclosed in a glass bulb 
from which the air has been exhausted, thereby preventing 
combustion of the filament. The current is passed through 
the filament and heats it to a state of incandescence. Fig. 
69 depicts a carbon filament lamp. Of the electric energy 
expended in this type of lamp, only about 5 per cent is repre- 
sented by the light emitted, while the balance appears as heat, 
so that such a lamp, while convenient, is not an efficient 
source of illumination. The heating effect of the current is 
also utilized in the various electric cooking utensils on the 
market, in electric welding, electric smelting, and in reducing 
metals from their ores. 

78. Magnetic Effect. — A wire carrying a current of elec- 
tricity deflects a magnetic needle. When insulated and coiled 



74 



LESSONS IN PRACTICAL ELECTRICITY 



Oxygen,! Parts 



around an iron core the current magnetizes the core. If the 
current flowing through a wire be sufficiently strong, the wire 
will attract iron filings, proving the existence of the magnetic 
field around the wire. This effect is very important and is 
treated under Electromagnetism, Lesson XIII. 

79. Chemical Effect. — We have noted in a simple voltaic 
cell (H 36) how electrolytic decomposition takes place inside 
the cell when a current is flowing. The current is also cap- 
able of decomposing certain 
chemical compounds (liq- 
uids) outside of the cell, 
when it is passed through 
them, breaking up the com- 
pounds into their constit- 
uent parts. Liquids may 
be divided into three classes : 
(1) Those which do not con- 
duct electricity at all, such 
as many of the oils, particu- 
larly petroleum; (2) liquids 
which conduct without decom- 
position, as mercury and 
molten metals, which con- 
duct just as solids; (3) 
liquids which are decomposed 



Connector- 




Hydrogen, 
-Z Parts 



Acidulorted 
- Water 



Copper.. 
Wire ' 



Pinch 
Cocl< 



Parts of 
Electrode 



Fig. 70. — Glass U-Tube with Electrodes 
Forming an Electrolytic Cell. 



when they conduct a current, as the dilute acids, solutions of 
metallic salts and some fused compounds. 

Experiment 31. Electrolysis of Water. — Fill the U-tube (Fig. 70) 
with water, and add a few drops of sulphuric acid to make the liquid a 
better conductor. Connect the terminals of two bichromate cells joined 
in series (^ 115) to the two platinum terminals shown in the U-tube, so 
that the circuit from the cells will be completed through the acidulated 
water. Have the corks quite loose in the U-tube for the gases to escape. 
When the circuit is completed bubbles of gas immediately rise from both 
platinum plates, more, however, from the platinum plate connected with 
the negative pole of the battery. The gases may be collected separately 
by the forms of apparatus shown in Figs. 73 and 76, or collected together in 
one tube in the form shown in Fig. 74. 

During this electrochemical action the current decomposes 
the water, liberating hydrogen gas at the negative battery 



EFFECTS PRODUCED BY THE ELECTRIC CURRENT 75 

pole and oxygen gas at the positive battery pole. Twice as 
much hydrogen as oxygen gas is liberated. ^ Water is com- 
posed of these two gases, hydrogen and oxygen, in the pro- 
portion of two parts of hydrogen to one of oxygen (or H2O) 
and the current breaks up the water into its constituent parts. 
If brass or copper plates are used, the plate connected with the 
positive battery pole will be attacked by the action, and no 
oxygen will be evolved. 

Experiment 32. — Reverse the direction of the current through the 
solution, by changing the battery terminals, and note that the hydrogen 
and oxygen gases are now liberated on the opposite electrodes from Experi- 
ment 31. This is another reason for supposing that the current has direc- 
tion, the opposite deflections of the magnetic needle being a former proof. 

80. Electrolysis. — A large number of chemical compounds 
in a state of fusion, or dissolved in certain solvents, can, like 
the acidulated water, be separated into their constituent 
parts by the passage of an electric current through them. 
Any substance that is capable of being decomposed by an 
electric current is called an electrolyte (as in a voltaic cell) and 
the process is termed electrolysis (meaning loosening by elec- 
tricity). Plates of carbon, lead, platinum, or other metals 
are used to conduct the current to and from the solution, 
according to the substance to be electrolyzed. 

These plates are called electrodes, and the plate by which 
the current enters the electrolyte is called the positive elec- 
trode or anode and the plate by which it leaves the solution 
is called the negative electrode or cathode. The constituent 
parts of the electrolyte which are liberated at the surface of 
the electrodes are called ions, the ion liberated at the positive 
electrode being called the anion, and that which appears at 
the negative electrode the cation. Any vessel or apparatus 
used for performing or measuring electrolysis is called a voltam- 
eter. In the electrolysis of water hydrogen is the cation and 
oxygen the anion. 

81. Electrolysis of Copper Sulphate. — 

Experiment 33. — Fill the U-tube (Fig. 70) with a solution of copper 
sulphate, made by dissolving some copper sulphate crystals (bluestone) 
in water, and subject the solution to electrolysis, as in the case of the 
water, using platinum electrodes. Metallic copper is deposited upon 



76 



LESSONS IN PRACTICAL ELECTRICITY 



Experiment 34. 



the negative electrode, that is, the plate becomes copper-plated. Oxygen 
gas is liberated at the positive platinum electrode and sulphuric acid is 
formed. 

The chemical symbol for copper sulphate is CUSO4. By 
electrolysis it is separated into Cu (metallic copper) and SO4 
(sulphion). The Cu goes to the negative plate while the SO4 
combines with water in the solution to form H2SO4 (sulphuric 
acid), and oxygen gas is liberated at the + platinum plate, as 
before. If the action is allowed to continue for some time, all 
the metallic copper is taken from the solution and deposited. 
This will be noted by the solution changing from a deep to a pale 
blue, as the change gradually takes place from copper sulphate 
to sulphuric acid. The action is represented as follows: 
CUSO4 = Cu + SO4 

Sulphate of copper becomes copper and sulphion. 

SO4 + H2O = H2SO4 + O 
Sulphion and water produce sulphuric acid and oxygen. 

Reverse the direction of current in Experiment 33 
and note that now the copper-coated plati- 
num plate becomes the positive electrode, 
with a platinum plate for the negative elec- 
trode. The latter has metallic copper de- 
posited upon it, while the former metallic 
copper on the positive plate is returned 
again to the solution. 

Experiment 35. — Substitute two copper 
electrodes for the platinum electrodes and 
repeat Experiment 33. Metallic copper is 
again deposited upon the negative electrode 
(increasing its weight), but from the posi- 
tive electrode no gas is evolved, yet this 
plate wastes away, or is dissolved in the 
solution, thereby losing in weight. 

When a copper positive plate is used 
(Fig. 71), the CUSO4 is separated into 
Cuj which is plated on the negative 
plate, and SO4, which attacks the 
positive plate and forms a new mole- 
cule of CUSO4 (copper sulphate). 
Thus as a molecule of copper sulphate is decomposed, a new 




Fig. 



Copper Sulphate 

71. — Copper Vol- 
tameter. 



EFFECTS PRODUCED BY THE ELECTRIC CURRENT 77 

molecule is formed, keeping the solution of constant strength. 
Just as much metalHc copper is thrown down into solution 
from the positive plate as is taken from the solution and de- 
posited on the negative plate. The art of electroplating is 
based on the above experiments. 

82. Electrolysis of Zinc Sulphate. — 

Experiment 36. — Dis-:olve some crystals of zinc sulphate (ZnS04, 
white vitriol) in water. Refill the U-tube (Fig. 70) with this solution and 
subject it to electrolysis. Use platinum electrodes and metallic zinc is 
deposited upon the negative electrode and oxygen gas is evolved from 
the positive electrode. Reverse the direction of current. The previously 
deposited zinc goes again into solution, while the other electrode now 
receives a deposit of zinc. Oxygen gas is not evolved from the positive 
electrode till all of the zinc has been thrown dowTi into solution. 

Experiment 37. — Repeat Experiment 36, using two zinc strips as 
electrodes, and note that the positive strip wastes away and the negative 
zinc strip gains in weight. The action of the Edison electrolytic meter j 
formerly used for measuring current, is dependent upon this principle; it 
was a zinc voltameter. 

83. Electrolysis of Lead Acetate. — 

Experiment 38. — Prepare a solution of lead acetate, and pass it through 
"filter paper to clear the solution. Fill the U-tube (Fig. 70) and subject it 
to electrolysis, using platinum electrodes. Metalhc lead is deposited at 
the negative plate and oxygen gas appears at the positive plate. In addi- 
tion to coating the platinum plate the lead will be deposited in a beautiful 
tree-like form extending out into the solution from the negative plate. 
The solution becomes weaker as the extraction of metallic lead continues. 
When the current is reversed the former positive plate receives the deposit 
in the "tree form," but oxygen gas is not now liberated from the positive 
plate, until the lead previously deposited is dissolved in the solution. This 
experiment is very suitable for illustration in a lantern projection cell, 
as well as for laboratory work. 

84. Electroplating. — The art of depositing a coating of 
metal upon any object is termed electroplating, and is based 
upon the principles of electrolysis already explained. The 
metal held in solution is always deposited on the object to be 
plated, which must be connected to the negative pole of the 
source of electricity, while a plate of the metal from which 
the coating is derived, as nickel, copper, gold, or silver, is used 
as the positive plate. In plating with gold or silver the bath 
(electrolyte) is always alkaUne, and generally a cyanide of 



78 LESSONS IN PRACTICAL ELECTRICITY 

the metal to be deposited is used for the solution. In plating 
an iron spoon with silver, for example, the iron is cleaned, to 
remove all dirt and grease, and then first receives a deposit 
of copper in a copper bath, as silver will not deposit upon iron. 
Articles of iron, steel, zinc, tin, and lead 'cannot be silvered 
or gilded unless first coated with a thin covering of copper. 
After having been coated with copper, the spoon is transferred 
to a silver bath, properly connected up, and a coating of the 
desired thickness deposited, after w^hich it is cleaned and bright- 
ened on a buffing wheel. 

Other substances beside metals can be electroplated by 
first preparing the surface with a coating of powdered graphite, 
or plumbago, upon which metal can be deposited. 

The character of the deposit depends upon the density or 
strength of curren1> per square inch used (H 100). If electro- 
lytic action takes place too rapidly, the deposit is soft, coarse- 
grained, and liable to prove unsatisfactory, while a small current 
gives a good, hard, close-grained deposit. A very low voltage 
is used in electroplating, the potential varying with the electro- 
lytes used. The following voltages have been given as most 
suitable for the different metals. 

Copper in sulphate 1.5-2.5 volts 

Copper in cyanide 4.0-6.0 volts 

Silver in cyanide LO-2.0 volts 

Gold in cyanide 0.5-3.0 volts 

Nickel in sulphate 2.5-5.5 volts 

85. Electrotyping. — Suppose an electrotype is desired from 
a column of standing type. An impression in wax, or plaster 
of Paris, is carefully made of the type, and the wax mold 
dusted over with powdered graphite to make the surface a 
conductor. The mold is connected as the negative plate in 
a copper plating bath and receives a thin coating of metalHc 
copper. After removal from the bath the copper deposit is 
removed from the mold and backed, or filled in, with type 
metal to about the depth of one-eighth inch. When cool, 
the back is planed smooth, fastened to a block of wood, and 
can then be used in the press. The copper mold is generally 
so thin that it is necessary to back it up with the type metal, 
owing to the pressure to which the electrotype is later sub- 




EFFECTS PRODUCED BY THE ELECTRIC CURRENT 79 

jected. In this manner the electrotypes for the pages of many 
books are made from the standing type and may be used for 
taking thousands of impressions. 

86. Polarity Indicator. — The positive and negative poles 
of a direct-current electric light, or power circuit, can be deter- 
mined by dipping the terminals, at some little distance apart, 
into a tumbler of water. As twice as much hydrogen gas is 
evolved at the negative wire as oxygen at the positive wire 
the polarity of the circuit is readily determined. Care must 
be taken not to bring the wires 
into contact, or some damage 
would occur, due to too much 
current flowing through such p^g 72. - Polarity Indicator, 
a low-resistance circuit. A 

solution of iodide of potassium, with a little starch added, is 
sometimes sealed in a glass tube and terminals are provided 
by which a current can be passed through and the polarity 
of the circuit determined. This is called a polarity indicator. 
Iodine is liberated at the positive terminal and turns the starch 
blue around this terminal. Fig. 72 shows the form of a com- 
mercial polarity indicator now in general use, the liquid turns 
red at the negative terminal. 

QUESTIONS 

1. Name all the effects of an electric current and give a commercial 
application of each. 

2. Explain the principle of an electric incandescent lamp. 

3. How would you classify liquids according to their conducting power 
and the chemical effect of the current upon them? 

4. What is an electrolyte? What is electrolysis? 

5. Define the terms anion, cathode, anode, cation. 

6. Describe the action in the copper voltameter, and give a sketch. 

7. Give two reasons for inferring that current has direction. 

8. What is the action in a copper voltameter when a platinum plate 
is substituted for a copper plate? Give sketch. 

9. What is a polarity indicator, and how is it used? 
10. State how an electrotype is made. 



LESSON VII 
MEASUREMENT OF CURRENT 

Strength of Current — Variation of Current and of the Current's Effects — 
How the Effects Vary with the Current Strength — Variation of 
Effects with the Same Current Strength through Dissimilar Appara- 
tus — Measurement of Current Strength — Definition of the Unit 
of Current Strength — Definition of a Unit Quantity of Electricity 

— The Ampere-Hour — Weight Voltameters — Voltameter Calcu- 
lations — Construction of the Gas Voltameter — Directions for 
Using the Gas Voltameter — Measuring Current Strength by a Gas 
Voltameter — Current Strength Used in Electroplating — Table VII 

— Questions and Problems. 

87. Strength of Cmrent. — The magnetic, the heating, or 
the chemical effect of an electric current may be employed to 
determine whether a current is flowing through a wire. If 
the magnetic effect of a current flowing through a wire is 
greater than that of another current, the intensity of the cur- 
rent, or the strength of the current, must be greater, since 
the magnitude of any of the current's effects varies with the 
current assumed to be flowing. We express the rate of flow 
of water through a pipe as so many gallons per second, which 
expression includes a definite quantity of water and a unit of 
time; that is, at a rate of flow of one gallon per second, we 
mean that one gallon passes any point in the pipe once every 
second. By the strength of an electric current we mean the 
rate of transfer of electricity past any point in the circuit in 
a unit of time (the second). It is obvious that the magnitude 
of the effects of the current may be used to measure the strength 
of the current. 

88. Variation of Current and of the Current's Effects. — 

Experiment 39. — Pass a current under a force of one volt through a 
coarse- wire galvanometer and note the deflection. Repeat the experi- 
ment with twice the applied pressure, two volts, and the deflection of the 
magnetic needle is less than twice as much as before, although the force 
is doubled and the current strength, varying as the force, must also have 
been doubled. 

80 



MEASUREMENT OF CURRENT 



81 



Experiment 40. — With an applied pressure of 4 volts note the amount 
of gas liberated from dilute sulphuric acid in 2 minutes by the appara- 
tus shown in Fig. 73. Repeat the experiment 
with 8 volts, and note that in the same time 
twice the volume of gas is generated. 

Experiment 41. — Using copper sulphate 
and two copper plates, carefully weighed 
before the test, apply a force of 2 volts for 10 
minutes and then reweigh the plates. The 
negative plate has gained in weight exactly 
what the positive plate has lost. Repeat the 
experiment with 4 volts for the same length of 
time and the change in weight is increased to 
double what it was before. 

Experiment 42. — Wind a number of turns 
of No. 30 iron wire around the bulb of a ther- 
mometer and place it in a small test tube con- 
taining a measured quantity of water. Place 
the test tube in a larger vessel containing saw- 
dust to prevent heat radiation. Apply a force 
of 4 volts for 10 minutes and, by aid of the 
thermometer, note the rise in the temperature 
of the water. Repeat the experiment with 8 
volts for the same period of time, with the 
same quantity of water, and at the previous 
starting temperature. Neglecting the heat lost 
by radiation, the increase of temperature is 
nearly four times as great as in the first test, 
although the current was only doubled. If the 
current had been tripled, the temperature rise 
would have been 9 times as great, and with the 
current quadrupled the rise would have been 16 times as great, and so on 




Student's Gas 



Voltameter. 



Shows decomposition of water 
into Hz and O. 



89. How the Effects Vary with the Current Strength. — The 

above experiments may be made simultaneously when the cir- 
cuit is arranged as in Fig. 74, in which nearly all the effects of 
the current are represented. The circuit is made up as follows: 
starting from the positive battery terminal the current would 
flow (1) through a few turns of coarse wire in the galvanometer 
coil; (2) a large number of turns of coarse wire on the spools of 
the electromagnet ; (3) a dilute solution of sulphuric acid in the 
mixed gas voltameter, the current to pass between platinum 
electrodes; (4) a solution of copper sulphate, the current to pass 
between copper electrodes; (5) a number of turns of fine iron 
wire wound around the bulb of a thermometer and immersed 



82 



LESSONS IN PRACTICAL ELECTRICITY 



in a vessel of water placed in sawdust; (6) through the carbon 
filament of an incandescent lamp; (7) through a switch to the 
negative pole of the battery, and (8) from the negative pole of 
the battery through it to the positive pole. 

When the switch is closed, the current produces the following 
effects simultaneously: The magnetic needle is deflected; the 
keeper or armature is attracted by the electromagnet with a 
certain force in pounds; hydrogen and oxygen gas rise in the 
graduated test tube, displacing the acidulated water therein; 




Sawdust 



Cells In Series 



Calori'mefer 



Incandescent Lamp 
Fig. 74. — The Effects of the Electric Current. 

This is a simple series circuit and the current is the same in all parts of it. 

metallic copper is dissolved from the copper positive plate and 
deposited upon the copper negative plate, so that it thereby 
gains in weight; heat is evolved in the vessel containing the 
coil of iron wire; light is given off by the incandescent lamp; 
zinc is being consumed in the battery furnishing the electrical 
energy to produce all the effects enumerated outside of the 
battery. 

All the effects commence at the instant the switch is closed, 
but only four can be noted instantly — the needle's deflection, 
the attractive force of the magnet, the evolution of gas, and the 



MEASUREMENT OF CURRENT 83 

brilliancy of the lamp. The weight of copper deposited and of 
gas liberated, and the number of degrees rise in temperature, 
due to a current flowing for only an instant, are so small as to be 
practically unmeasurable. By allowing the current to flow for 
a certain period of time a measurable quantity is obtained, 
which, divided by the time in seconds, gives the magnitude of 
the effect per second. Keep the switch closed for about five 
minutes (5 x 60 = 300 seconds) ; then, by dividing the volume 
of gas generated in 300 seconds by 300, we obtain the gas gen- 
erated per second, and similarly with the gain in temperature 
and the gain in weight of the negative copper plate. 

We thus get a series of results of the different effects all cor- 
responding to the same strength of an electric current, flowing 
for a unit of time. The intensity of current that deflected the 
needle in one part of the circuit, or magnetized the iron core of 
the electromagnet, is exactly the same as that which decomposed 
the acidulated water or the copper sulphate, or heated the iron 
wire. This is a simple series circuit, although made up of a 
number of different conductors, and the current is the same in 
all parts of a series circuit; that is, the rate of flow past any, 
point selected is the same. The order of the arrangement of 
the apparatus is also immaterial. By increasing the E. M. F. 
of our battery so that twice the pressure is applied to this same 
circuit, we double the current strength or rate of flow. The 
switch is closed for the same time as before, and the results 
noted for comparison. A third test may also be made, using 
three times the force. The record of three such tests, with ap- 
paratus as arranged in Fig. 74, is approximately as foflows: 

Tests of Current Effects 

Test 1 Test 2 Test 3 

Galvanometer, deflection in degrees 25 37 42 

Electromagnet, pounds pull 5.4 9.5 13 

Gas voltameter, cubic centimeters of gas gener- 
ated per second 0.17 0.34 0.51 

Copper voltameter, gain in grams per second . . 0.0003 0.0006 0.0009 

Calorimeter, degrees rise per second 0.1 0.4 0.9 

Incandescent lamp, candle-power 1.5 5 25 

From the above tests the following facts will be noted: The 
deflection of the galvanometer needle is not directly proper- 



84 LESSONS IN PRACTICAL ELECTRICITY 

tional to the current, for doubling the current does not double 
the deflection. The attractive force of the magnet is not quite 
directly proportional to the current strength. The volume of 
gas generated is exactly proportional to the current, and if 
the current had been quadrupled the gas generated per second 
would have been four times as great, and so on. The deposit 
of copper is directly proportional to the current, doubling the 
current, also doubling the gain in weight. The rise in tem- 
perature of the calorimeter for twice the current strength was 
more than doubled, in fact it was increased fourfold; with 
three times the current strength the rise is ninefold — the tem- 
perature rise thus increases directly as the square of the current 
strength. The luminosity of the lamp increased very rapidly 
with the current. 

90. Variation of Effects with the Same Current Strength 
through Dissimilar Apparatus. — If the series circuit. Fig. 73, 
had contained two pieces of each apparatus of widely varying 
dimensions of plates, convolutions in the coils, size of wire, etc., 
what would have been the result? The current strength would 
have been the same in each part of the circuit as before. The 
galvanometer of many turns would produce a larger deflection 
than one of few turns of the same diameter. The electromag- 
net, with the greater number of turns, would have the greater 
attracting power. A gas voltameter with small plates, widely 
separated, would evolve the same volume of gas as a voltameter 
with much larger plates placed close together, since the gas 
evolved is proportional only to the rate of flow of electricity, 
which is the same through both voltameters, and hence inde- 
pendent of the size and separation of the electrodes. Similarly, 
in two copper voltameters in the same series circuit, the weight of 
copper deposited is independent of the size of the plates or their 
distance apart, and would be the same for each voltameter, 
however constructed. More heat would be generated by the 
coil of many turns of fine wire than by the coil of few turns 
because of its higher resistance. The current flowing through 
a circuit is the same in all parts of that circuit; thus, if at two 
different points in a circuit a gas voltameter be inserted, the gas 
evolved at the one point will be exactly equal to that evolved 
at the other point. 



MEASUREMENT OF CURRENT 85 

91. Measurement of Current Strength. — To compare dif- 
ferent strengths of current some arbitrary standard must be 
adopted. If we defined our unit of current as one of such 
strength as to deflect our magnetic needle (H 89) 25 degrees, it 
would be necessary to specify the length of needle, diameter of 
coil, number of turns, place where the needle was set up, etc.; 
these cumbersome specifications would make a unit so defined 
an impractical standard. Also, in the case of the electromagnet, 
all the dimensions of the core and keeper and of the wire, qual- 
ity of the iron, etc., would have to be stipulated. If we would 
express the unit of current strength as such a rate of flow that 
would attract a keeper with a force of 5.4 pounds, then again 
2 units of current would not attract the keeper with a force of 
10.8 pounds, as might be expected, but only of 9.5 pounds, 
(see test, If 89). The current strength is directly proportional, 
however, to the amount of gas generated per second or the 
amount of metal deposited per second, so that of all the effects 

,the chemical one is the best adapted for furnishing a standard 
unit of current strength, since such a standard will be indepen- 
dent of the apparatus used to produce the effect. The heating 
and magnetic effects are employed in various practical instru- 
ments for measurements, but they are standardized by the 
chemical effect. 

92. Definition of the Unit of Current Strength. — The 
strength of current is directly proportional to the amount of 
chemical decomposition it can produce in a given time. That 
steady current which, when passed through a solution of nitrate 
of silver in water, in a silver voltameter, deposits silver at the rate 
of 0.001118 gram per second, is taken as a unit of current strength 
and called one ampere. 

One ampere will deposit in one second: 

0.0003293 grams of copper in a copper voltameter; 
0.0003387 grams of zinc in a zinc voltameter. 

One ampere will also decompose 0.00009334 grams of dilute 
sulphuric acid per second. One ampere will also evolve 0.1733 
cubic centimeters of mixed gas per second in a gas voltameter 
(when the temperature is 0° Centigrade and the atmospheric 
pressure is 76 centimeters of mercury). 



86 LESSONS IN PRACTICAL ELECTRICITY 

93. Definition of a Unit Quantity of Electricity. — Distinc- 
tion must be made between the total quantity of electricity 
that passes through a circuit in a given time and the rate of 
flow of electricity during that time. For example, at the rate 
of flow of one gallon per second, 3600 gallons of water would 
be delivered to a tank in an hour, the total quantity being 
readily distinguished from the rate of flow. We might take the 
gallon per second as a unit of rate of flow and name it, but this 
has not been done in hydraulics, although it is done in the case 
of electricity. The total quantity of water equals the rate 
multiphed by the time in seconds; thus, at a rate of flow of 
8 gallons per second, in 60 seconds the total quantity delivered 
would be 480 gallons, which same quantity could be delivered 
to a tank in one second if the rate were 480 gallons per second, 
or in one half second if the rate were 960 gallons per second, or 
in 480 seconds if the rate were only one gallon per second. 
Similarly the unit quantity of electricity is the amount of electricity 
that flows per second past any point m a circuit when the current , 
strength is one ampere, and this unit quantity has been called the 
coulomb. If a current of one ampere flows for 60 seconds, 
then the total quantity is 60 ampere-seconds, or 60 coulombs 
of electricity. 

First: To find the total quantity of electricity in 
coulombs passing through a circuit in a given time .* 

Multiply the current strength (expressed in amperes) by the time 
(expressed in seconds). 

Let I = current in amperes, 

Q = total quantity of electricity in coulombs, 
t = time the current flows in seconds. 
Then, since 

quantity = current strength x time, 
or coulombs = amperes X seconds, 

it follows that r\ r x ^in\ 

<4 = iXt (Ibj. 

Problem 14. — An incandescent lamp requires a current of one half 
an ampere to maintain its proper brilliancy. If the lamp is illuminated 
for two hours what quantity of electricity will traverse the lamp? 
- t == 2 hours = 60 X 60 X 2 = 7200 seconds. 
By Formula (16) Q = I x t = | x 7200 = 3600 coulombs. 



MEASUREMENT OF CURRENT 87 

Second: To find the average current strength (in 
amperes) when the time of current flow and the quan- 
tity OF electricity are known: 

Divide the quantity {in coulombs) by the time (in seconds). 
Current strength = quantity -=- time, 
or amperes = coulombs -^ seconds, 

whence, 1 = ^ (17). 

tr 

Problem 15. — What is the average current in a lamp circuit if the 
quantity of electricity traversing that circuit in 5 hours is 54000 coulombs? 

5 hours = 60 X 60 X 5 = 18000 seconds. 

^ r? 1 n-^ T Q 54000 ^ 

By Formula (1/) 1 = -2 = = 3 amperes. 

^ ^ ^ t 18000 ^ 

Third: To find the time (in seconds) required for 
a given quantity of electricity (in coulombs) to pass 

A POINT IN A circuit: 

Divide the quantity of electricity (in coulombs) by the rate of 
flow (in amperes). 

quantity 



Time = 



current strength' 
coulombs 



or seconds - , 

amperes 

or, by substitution, ^ ^j (^^)' 

Problem 16. — How long a time will be required to pass 18000 cou- 
lombs through an electroplating bath if the average current strength 
is 6 amperes? 

By Formula (18) t = ^ = -^^^ = 3000 seconds, or ^^^ = 50 minutes. 
16 60 

94. The Ampere-Hour. — The coulomb is a very small unit 
of quantity. A larger unit, the ampere-hour, is often used. 
One ampere-hour would be the quantity of electricity that would 
pass any point in a circuit in one hour, when the strength of 
current is one ampere. One ampere-hour obviously equals 2 



88 



LESSONS IN PRACTICAL ELECTRICITY 



amperes for one-half hour; 4 amperes for one-quarter hour, or 
one-quarter ampere for 4 hours, and so on. One ampere-hour 
also equals 3600 coulombs. 

The capacity of batteries is rated in ampere-hours. For ex- 
ample, a 100-ampere-hour cell would mean one in which suf- 
ficient chemicals were present to maintain 10 amperes for 10 
hours; 5 amperes for 20 hours, etc. An ampere-hour record- 
ing meter may be placed in a circuit to record the total quantity 
of electricity that has been utilized, or the total ampere-hours. 

Problem 17. — A current of 6.5 amperes was maintained by a cell for 
4 hours. What quantity of electricity has been used? 

Quantity = amperes x hours = 6.5 x 4 = 26 ampere-hours. 

Suppose the cell has a capacity of 80 ampere-hours, how long could 
the above current be maintained? 



Hours 



ampere-hours 80 



amperes 



— = 12.3 hours. 
6.5 



95. Weight Voltameters. — Current strength may be de- 
termined by a weight voltameter, one in which the weight of 

metal deposited or weight of 
water decomposed serves to 
determine the rate of flow, or 
by a gas voltameter, in which 
the volume of mixed gas to 
be evolved is used to deter- 
mine the current strength, 
A weight voltameter is illus- 
trated in Fig. 75; the plates 
are supported by arm A 
which can be rotated about 
the swivel B. The two out- 
side plates form the anode, 
and are joined to one binding 
post, while the cathode is 
placed between them and 
connected to the other bind- 




- Construction of a Weight 
Voltameter. 

One cathode between two anodes. 



ing post. The cathode thus receives a deposit on both sides. 
An adjustable arm controlled by pinion P serves to lower the 
plates into the electrolyte. 



MEASUREMENT OF CURRENT 89 

96. Voltameter Calculations. — First : To calculate the 

STRENGTH OF AN UNKNOWN CURRENT (iN AMPERES) WHICH 
HAS PASSED THROUGH A WEIGHT VOLTAMETER: 

Find the weight of metal deposited per second by dividing the 
total gain in weight by the time {in seconds) the current flows 
through the instrument; divide this quotient by the weight depos- 
ited by one ampere in one second. 
Let I = current in amperes, 
W = total gain in weight, 
t = time of current flow in seconds, 

K = mass deposited by one ampere in one second, that is 
by one coulomb. 
Substituting for the above statement: 
weight gained 



Amperes = 



gain per coulomb x time' 



W 

'-w^f (^9^- 

If W is expressed in grams: 

K for a copper voltameter is 0.0003293 gram, 
K for a zinc voltameter is 0.0003387 gram, 
K for a silver voltameter is 0.001118 gram, 
K for nickel voltameter is 0.000304 gram, 
K for a sulphuric acid weight voltameter is 0.00009334 gram, 
K for a sulphuric acid gas voltameter is 0.1733 cubic cen- 
timeter. 

Problem 18. — The negative plate of a copper voltameter has increased 
in weight by 1.818 grams in thirty minutes. What was the average 
current strength? 

K for copper is 0.0003293, t = 30 minutes = 30 X 60 = 1800 sec. 

By Formula (19) I = ^ = 0.0003293x180 = ^'"^^ '^"P^^^' 
Second: To find the weight of any metal that will 

be" deposited in a voltameter by a GIVEN CURRENT IN 
A GIVEN time: 

Multiply the current strength by the time {in seconds) and this 
product by the weight deposited by one ampere in one second (K) ; 



90 LESSONS IN PRACTICAL ELECTRICITY 

the result is the weight expressed in grams (one pound = 453.59 
grams) . 

Weight (gained) = current x time x K, 

or .W = IxtxK (20). 

Problem 19. — In an electroplating bath how many g^ams of zinc will 
be deposited by a current of 5 amperes in 45 minutes? 

K for zinc = 0.0003387, t = 45 minutes = 45 x 60 = 2700 seconds. 
By Formula (20) W = IxtxK = 5x 2700 x 0.0003387 = 4.572 grams. 

Third: To find the time required to electrolyt- 

ICALLY deposit ANY GIVEN WEIGHT OF METAL WITH A GIVEN 

current: 

Divide the weight hy the current strength, and by the weight de- 
posited by one ampere in one second (K) ; the result is the time 
expressed in seconds. 

weight (gained) 



Time = 



current x K 



W 

or t (seconds) =— — (21). 

J. X -tv 

Problem 20. — How long a time will be required to deposit 5.93 grams 
of silver on a copper-plated teaspoon with a current of 2 amperes? 

K for silver = 0.001118 gram. 

Bv Formula (21) t = = — = 2652 seconds, or 

oy rormuid (,z,iy u ^^^ 2x0.001118 60 

= 44 minutes 12 seconds. 

97. Construction of the Gas Voltameter. — The gas vol- 
tameter is convenient for individual laboratory use with a large 
body of students, as it obviates the necessity of a pair of scales 
for each student. A demonstration type of instrument is shown 
in Fig. 76. The battery terminals, T, lead to the platinum 
electrodes, Pt. Dilute sulphuric acid is poured in at F and is 
decomposed by the current into H and O, these gases may be 
removed for test by opening the stopcocks, SC. 

A student's voltameter is illustrated in Fig. 73 and is com- 
posed as follows: 



MEASUREMENT OF CURRENT 



91 



H^SO; 



1 metal stand (16 inches high) 

1 glass U-tube 

2 platinum electrodes sealed in a glass tube and connected by a copper 
wire, to which connectors are attached 

2 rubber stoppers or corks for electrodes 

1 glass burette, graduated from to 20 cubic centimeters and reading 
in tenths of a cubic centimeter 

2 adjustable clamps 

8 inches of rubber tubing 
2 brass connectors. 

98. Directions for Using the Gas Voltameter. — 

(1) Attach both clamps to the stand. (2) Attach one end of the rubber 
tube to the glass U-tube and carefully clamp it by 
the lower clamp on to the stand. (3) Attach the 
other end of the rubber tube to the burette and 
carefully clamp it by the upper clamp. (4) Ad- 
just the position of both clamps so that the zero 
mark on the burette is about one half inch 
below the level of the top of the U-tube. (5) 
Pour the acidulated water into the mouth of the 
burette till the water in the U-tube is about one 
half inch from the top; the height of liquid in the 
burette should be on a level with or above the 
zero mark. (6) With the electrodes inserted 
through the corks, place each one in position care- 
fully, by giving a slight twist to the right as the 
cork enters. (7) The water level in the U-tube 
and burette should now be the same, or further 
adjustment must be made to attain this result. 
The water level in the burette does not necessarily 
have to correspond with the zero graduation, but 
must not be below it. (8) Unclamp the burette 
and hold it nearly horizontal. The liquid will not 
run out if the corks are tight, so that this is an 
air leakage test. (9) Attach the connectors to the 
wires from the source of E. M. F. (which should 
be 2 or more volts); a switch is preferably included in the circuit. 

In electrolyzing any substance a back or contrary E. M. F. 
is set up in opposition to the decomposing current, due to the 
chemical affinity of the substances disunited, which tend to re- 
unite. Sufficient force must therefore be applied to overcome 
this force of chemical affinity. For example, in the case of 
water this opposing force is about 1.5 volts, so that it requires 
a greater force than 1.5 volts to electrolyze water, hence two 
cells are joined in series. 




Battery 

Fig. 76. — Gas Vol- 
tameter. 

Hoffman's lecture-room 
form. 



92 LESSONS IN PRACTICAL ELECTRICITY 

Experiment 43. — Close the switch connecting the above voltameter in 
circuit. Bubbles of gas rise in the U-tube from both electrodes, displace the 
water, and force it up the burette. Twice the volume of gas (hydrogen) 
is collected over the negative electrode than is collected over the positive 
electrode (oxygen). Run the test till the volume of hydrogen gas occu- 
pies nearly the whole limb of the U-tube, when the switch should be opened. 

Experiment 44. — With the gases collected in Experiment 43, lower the 
burette as far as possible (to decrease the hydrostatic head). Remove the 
cork for an instant from the hydrogen limb and quickly apply a lighted 
match. The hydrogen burns with a pale bluish flame. Replace the cork 
quickly so that the solution is not forced out of the U-tube. Now remove 
the cork from the oxygen limb, extinguish the flame of the match, and quickly 
apply the glowing spark to the oxygen; the match immediately bursts 
into a flame again. Re-place the cork quickly. Oxygen gas does not burn, 
but supports combustion. If both gases are collected in a single tube, as 
in the form of voltameter shown in Fig. 74, and a lighted match is pre- 
sented to the mouth of this tube the hydrogen, instead of burning, 
explodes with a violent report, due to the presence of the oxygen. 

99. Measuring Current Strength by a Gas Voltameter. — 

To FIND THE CURRENT STRENGTH WHEN A DEFINITE VOLUME 
OF GAS IS EVOLVED IN A GIVEN TIME! 

Divide the volume of gas evolved by the time (in seconds) and 
this quotient by the volume of gas evolved by one ampere in one 
second (K). The result is the current in amperes (subject to 
corrections when greater accurac}^ is required) .^ 

^ , . ■ cu. cm. of gas generated 

Current m amperes = : — - — ^^- — — , 

time (seconds) x K 

or I = -^^ (22). 

.t XK 

K for the mixed gases from water or the two gases evolved 
separately = 0.1733 cubic centimeters ( H 92). 

The volume of gas (in cubic centimeters) which will be evolved 
by a given current in a given time is 

volume evolved (cu. cm.) = current x time (seconds) x K, 
or V = IxtxK (23). 

Also the time required to evolve a certain quantity of gas 
with a given current is 

'^ih ''''■ . 

^ Neglecting temperature, barometric pressure and hydrostatic head. 



MEASUREMENT OF CURRENT 93 

Experiment 45. — Set up the gas voltameter again according to the 
directions in ^ 98. To correct the error caused by the decrease in volume of 
the gases, due to the weight of the liquid in the burette at the end of the 
test, lower the burette before the test so that the height of liquid in it is 
about on a level with the bottom of the U-tube. Secure a watch (prefer- 
ably with a second hand). Note the level of the Hquid on the burette 
scale before starting the test. Close the switch, noting the exact time. 
Allow the gas to be evolved till either the hydrogen hmb of U-tube is 
nearly full, or the Hquid in the burette approaches the end of the scale. Do 
not run above scale limit. Note the time of opening the switch, also the 
height of the liquid in the burette. 

Problem 21. — The following data are recorded in Experiment 45. Find 
the strength of current. 

Level in burette before test 2.6 cu. cm. 

Level in burette after test 28.8 cu. cm. 

Volume of gas evolved = 28.8 - 2.6 = 26.2 cu. cm. 

Time of closing switch 8.40. 

Time of opening switch 8.45. 

Length of run = 5 minutes = 5 x 60 = 300 seconds. 

26 2 
Volume of gas generated per second = — '— = 0.0873 cu. cm. 

oOO 

One ampere in one second (one coulomb) generates 0.1733 cubic centi- 

ns7^ 
meters of gas per second, therefore the current is -^ — = 0.5 ampere, 

U. 1 / oo 

V 26 2 

or by Formula (22) I = ^^^ = 0.1733x300 = "'^ '''^'^''- 

When more accurate calculations are desired the following 
formula is used to find the current strength: 

I = V X h X 273 

0.1733 X 76 (273 + C°)xt * ' ' * ^^^^• 

where V = volume of gas in cubic centimeters, 

h = height of barometer in centimeters of mercury, 
C° = temperature of room where test is made in de- 
grees Centigrade, 
t = time (in seconds) during which gas is evolved. 

Problem 22. — In an experiment the volume of gas generated in a gas 
voltameter was found to be 20 cubic centimeters in 50 seconds, its tem- 
perature (taken as the temperature of the room) being 20 degrees Centi- 
grade. The pressure of the atmosphere was equal to 75 centimeters of 
mercury. What was the current strength? 



94 LESSONS IN PRACTICAL ELECTRICITY 

By Formula (25) 

, 20x75x273 „,^ 

I = = 2.12 amperes. 

0.1733 X 76 (273 + 20) X 50 ^ 

To find the volume of gas generated by a known current 
use the formula: 

0.1733x1x76(273 + 0°) xt 

hx273 ■ ■ ■ ^ ^' 

Problem 23. — What volume of gas would be produced in a gas voltam- 
eter in 30 seconds by a steady current of 18 amperes, supposing the tem- 
perature of the gas so produced is 20 degrees C. and the barometer stands 
at 77.5 centimeters? 

^ t:^ 1 /o«N ir 0.1733 X 18 X 76(273 + 20) X 30 ^^ ,^ 

By Formula (26) V = = 98.49 cu. cm. 

/ / .o X .^/o 

100. Current Strength Used in Electroplating. — If the 

metallic deposition is performed too rapidly the deposit be- 
comes open and of a powdery appearance. A low current 
density produces a hard, close-grained surface. The usual den- 
sities used in practice as reckoned on the area to be plated are : 

Copper acid bath, 10 to 12 amperes per square foot. 
Copper cyanide bath, 6 to 8 amperes per square foot. 
Nickel, double sulphate, 4 to 6 amperes per square foot. 
Gold, chloride in cyanide, 1 to 2 amperes per square foot. 
Silver, double cyanide, 2 to 5 amperes per square foot. 

Problem 24. — A piece of sheet-iron, six inches square, is to be plated 
on both sides in a copper acid bath. What current strength is required? 
Area of plate (both sides) =6x6x2 = 72 square inches 

144 
= -—= 0.5 square foot. 

At 11 amperes per square foot, the required current is 5.5 amperes. 

Table VII. Approximate Values of Current Used in Commercial Apparatus 

For a 110-volt, 16-candle-power, carbon incandescent lamp . . 0.5 ampere 
For a 110-volt, 20-candle-power, ''Mazda" tungsten incandescent 

lamp 0.23 ampere 

For an enclosed 110-volt arc lamp 5 amperes 

For an open-air arc lamp . . . ." 8 to 10 amperes 

For a 220- volt 25-horse-power motor when fully loaded ... 94 amperes 

For a 110-volt fan motor ^ to 2 amperes 

For the average electric bell To ampere 

For the average telegraphic circuit 0.025 ampere 

For a 110-volt voltmeter, full-scale deflection 0.006 ampere 

For electric welding 20 to 50,000 amperes 



MEASUREMENT OF CURRENT 95 



QUESTIONS 

1. What do you understand by current strength? 

2. State some experiments you would make to ascertain how the 
effect of a current varies with its strength. 

3. Which effects of the current are directly proportional to it? 

4. Which effects do not vary directly with the current strength? 

5. An electromagnet attracts its keeper with a force of 18 pounds. 
If twice the E. M. F. be applied to the magnet coils, what will be the 
comparative result? 

6. A coil of iron wire carrying a current is placed into a tumbler 
of water for 10 minutes and the temperature is changed 6 degrees. The 
current is then exactly doubled and maintained for the same length of time. 
What is the change in temperature? 

7. Which is the most suitable effect of the current by which it can 
be measured? Give reason for your answer. 

8. What w^ould be the objection to considering as the standard unit 
of current strength one of such a strength that would deflect a galvanom- 
eter needle 30 degrees? 

9. What is the unit of current strength? A current is said to be 
5 amperes. What do you understand by this expression? 

10. Explain the difference between the terms "current strength" and 
"quantity of electricity." 

11. What is the unit of electrical quantity? Five coulombs pass every 
second through a lamp. What is the current strength? 

12. W^hy is it that you cannot electrolyze water with one Daniell cell? 

13. Platinum and copper plates are dipped into a solution of zinc sul- 
phate and a current is passed from the platinum to the copper plate. How 
are the plates affected? 

14. Copper and platinum plates are dipped into copper sulphate. 
What is the action when the current is passed from the copper to the 
platinum plate? 



PROBLEMS 

1. Hov/ many ampere-hours will be recorded by a meter through 
which 160 amperes are flowing for three quarters of an hour? Ans. 120 
ampere-hours. 

2. A 100-ampere-hour Edison-Lalande cell is discharged through 
an electromagnet at a 2| ampere rate. How long will the ceU maintain 
this current through the magnet? Ans. 40 hours. 

3. A meter records 500 ampere-hours. It was in circuit 5 days for 10 
hours each day. What was the average current used? Ans. 10 amperes. 

4. How many coulombs have passed through an arc lamp in three 
quarters of an hour if the current was 10 amperes? Ans. 27,000 coulombs. 



96 LESSONS IN PRACTICAL ELECTRICITY 

5. What current strength is required to deposit 5 grams of copper 
upon an iron spoon in 35 minutes? Ans. 7.219 amperes. 

6. A meter records 54,000 coulombs in 3 hours. What was the aver- 
age current? Ans. 5 amperes. 

7. How many grams of copper will be deposited on an iron plate 
used for a ship's hull in 10 hours if the average current is 25 amperes? 
Ans. 296.37 grams or 0.654 pound. 

8. The two terminals of an electric-hght circuit are dipped into a 
tumbler containing 5 grams of acidulated water. How long would a 
current of 3 amperes flow before the water was entirely decomposed? 
Ans. 4i hours 57 min. 35 sec. 

9. Using a current density of 5 amperes per square foot, how long a 
time is required to copper-plate both sides of a square iron plate meas- 
uring 4 feet on a side, supposing sufficient thickness is attained when 
the coating weighs 4 grams per square foot? Ans. 40 min. 29 sec. 

10. An inverted test tube, capacity 40 cu. cm., is filled with acidulated 
water, and the terminals of a battery having several cells in series are 
introduced underneath the tube. In 5 minutes half of the tube was filled 
by gas. What was the strength of current in the circuit? Ans. 0.384 
ampere. 

11. The negative zinc plate of an Edison electrolytic meter increased 
in weight, during a certain time, by 3.455 grams. This amount represents 
one one-thousandth part of the current used by the consumer. With 
how many ampere-hours should he be charged? Ans. 2833 ampere- 
hours. 

12. What bill would you render for the electricity used in Problem 11 
if the rate was 1.5 cents per ampere-hour? Ans. $42.50. 



LESSON VIII 

OHM'S LAW 

Electromotive Force (Pressure) — Electromotive Force of Batteries — 
Table- VIII — Ohm's Law — Circuits and their Resistance — Re- 
sistances in Series — Equal Resistances in Parallel (Joint Resistance) 
— Conductance of a Circuit — Unequal Resistances in Parallel — 
Conductance Method for Conductors in Parallel — Resistances 
Joined in Multiple-series — Division of Current in a Divided Cir- 
cuit — Ohm's Law Applied to a Battery Circuit — Questions and 
Problems. 

101. Electromotive Force (Pressure). — Electromotive force, 
wliich is the priniary cause of a flow of electricity, has been 
defined (^35) as the force which moves or tends to move 
electricity. The various terms electromotive force, pressure, 
difference of "potential, and voltage are frequently used to signify 
the same thing, namely, that force which moves, or tends to 
move, electricity against the resistance of a conductor. 

The electromotive force set up by a voltaic cell is the result 
of the difference of potential set up between the two plates and 
proportional to it. Just as in water pipes, where a difference 
in level produces a pressure which causes a flow of water the 
instant a valve is opened, so in an electric circuit a difference 
of potential produces an E. M. F. which sets up a current 
the instant the circuit is completed for the electricity to flow 
through. In the case of both water pipes and electric circuits 
there may be a great pressure and yet no flow of water or 
electricity. If the flow of water is prevented by a closed valve, 
there will be no flow or current so long as the valve is closed, 
yet there may be a high pressure. If the path of the electricity 
is stopped by a switch being open or by a broken wire, there will 
be no flow of current (amperes), so long as the switch is open, 
though the pressure (volts) may exist at the terminals of the 
battery or generator; in Fig. 37 there can be no flow of elec- 
tricity in the wire held over the magnetic needle until the 

97 



98 LESSONS IN PRACTICAL ELECTRICITY 

circuit is completed by closing the switch, yet there is a pres- 
sure between the switch points. 

There is one other factor, in addition to the pressure, that 
determines the amount of the current, both of water and of 
electricity. This factor is the resistance of the wires and elec- 
trical device in the case of electricity, and the resistance of 
the pipes and hydraulic device in the case of water. The 
greater this resistance the less the current under the same pres- 
sure. Resistance has been fully explained in Lesson V. 

If the voltage impressed on a circuit is increased, the cur- 
rent flow will be correspondingly increased, as would the flow 
of water through a pipe, if the water pressure causing the flow 
was increased. 

Experiment 46. — Connect a Daniell cell in series with spool No. 4 of the 
resistance set (H 67) and a detector galvanometer, and note the value 
of the deflection. Now substitute a bichromate cell for the Daniell cell, 
using the same spool, and the deflection is greater than before. The 
E. M. F. of the bichromate cell is higher than that of the Daniell cell, 
and therefore causes a larger current to flow through the same resistance. 
Any other type of cell used would cause more or less current to flow through 
the spool, depending upon its E. M. F. (pressure in volts). 

In a battery, the E. M. F. is dependent on the nature of the 
plates and the solution used, but independent of their size or 
distance apart. 

In a generator the E. M. F. is set up by revolving a bundle 
of wires in a magnetic field, and depends upon the strength 
of the field, the number of wires revolved, and the speed. 

102. Electromotive Force of Batteries. — The following table 
gives the electromotive forces of the different cells described 
in Lesson IV and of some others: 



Table VIII. E. M. F. of Batteries 

Bunsen 1.75 to 1.95 volts Grove . . . . 1.75 to 1.95 vo! 



Chloride of silver . 1.1 

Daniell 0.98 to 1.08 

Dry cell 1.4 

Edison-Lalande . . 0.7 

Grenet 1.8 to 2.3 



Leclanche . . .1.4 to 1.6 

Partz 1.95 to 2.0 

Smec .... 0.65 

Storage cell . . . . .2.1 
Edison storage cell . .1.2 



ts 



Generators may develop from a few volts to thousands of volts, accord- 
ing to the purpose for which they are designed. 



OHM'S LAW 99 

103. Ohm^s Law. — In any circuit through which a 

CURRENT IS FLOWING THE THREE FOLLOWING FACTORS ARE 

present: (1) The pressure or potential difference, ex-, 

PRESSED in volts, CAUSING THE CURRENT TO FLOW. (2) ThE 

OPPOSITION OR resistance of the circuit, expressed in 
ohms, which must be overcome. (3) The current strength, 
EXPRESSED IN ampcres, which is maintained in the cir- 
cuit, AS A RESULT OF THE PRESSURE OVERCOMING THE RESIS- 
TANCE. A DEFINITE AND EXACT RELATION EXISTS BETWEEN 
THESE THREE FACTORS, PRESSURE, CURRENT STRENGTH, AND 
RESISTANCE IN ANY CIRCUIT, WHEREBY THE VALUE OF 
ANY ONE FACTOR MAY ALWAYS BE CALCULATED WHEN THE 
VALUES OF THE OTHER TWO FACTORS ARE KNOWN. ThIS 

RELATION, KNOWN AS Ohm^s Law, IS very important, since 

IT FORMS THE BASIS FOR ALL CALCULATIONS IN ELECTRICAL 
ENGINEERING. It MAY BE SUMMARIZED AS FOLLOWS.* 

First. — • The current in any electric circuit is equal to the electro- 
motive force applied to the circuit, divided by the resistance of 
the circuit} 

Let E = E. M. F. or available pressure, expressed in volts, 
applied to any circuit, 
R = resistance of the circuit, expressed in ohms, 
I = current strength, expressed in amperes, to be main- 
tained through the circuit. 
Then, by the above statement of Ohm's Law, 
pressure 



current = 
or amperes = 



resistance' 
volts 
ohms' 
E 



1=^ '..... (27). 

The following five statements and formulae are directly 
derived from the above general statement of Ohm's Law, and 
are all therefore included in the expression I = E -^ R. 

1 Ohm's Law, as stated above, applies to direct currents flowing in 
any circuit. It is modified to some extent in alternating-current calcu- 
lations. See ^ 350. 



100 LESSONS IN PRACTICAL ELECTRICITY 

Problems are solved under each case to illustrate the inter- 
pretation of each statement made. 

Problem 25. — An incandescent lamp has a resistance (hot) of 220 ohms, 
and is connected to electric-light mains, across which 110 volts potential 
difference is maintained. What current will flow through the lamp? 
E 110 1 

By Formula (27) ^ " r " 220 ^ 2 ^"^P^^^' 

Second. — The current strength in any circuit increases or de- 
creases directly as the E. M. F., or potential difference, increases 
or decreases, when the resistance is constant. With a constant 
pressure the current increases as the resistance is decreased, and 
decreases as the resistance is increased. Briefly, the current 
varies directly as the E. M. F. and inversely as the resistance. 

E 

Since I = — , it follows that with R constant, I varies directly 

as E. With E constant the greater R, the less I, and vice versa. 

Problem 26. — In Problem 25, if the pressure is increased from 110 
to 220 volts, what current will the lamp receive, assuming the resistance 
constant? 

E 220 
By Formula (27) I = — = — — = 1 ampere. 
XV 220 

This problem illustrates the increase of I with increase of E with a 
constant R. 

Problem 27. — In Problem 25, if the pressure is reduced to 55 volts, 
what current will the lamp receive? 

By Formula (27) I ='^ = 220 = ^ ampere. 

This problem illustrates the decrease of I with the decrease of E when 
R is constant. 

Problem 28. — In Problem 25, if a lamp of 110 ohms resistance is used, 
what current will it receive? 

E 110 
By Formula (27) I = — = — — = 1 ampere. 
K 110 

With E constant, I increases as R decreases. 

Problem 29. — In Problem 25, if a lamp of 440 ohms is used, what cur- 
rent will it receive? 

T, T. 1 /^^N , E 110 1 

By Formula (27) I = — = — — = - ampere. 
[K 440 4 

Therefore, as R increases, when E is constant, I decreases. 



OHM'S LAW 101 

Third. — The electromotive force required to maintain a certain 
current strength in a circuit of known resistance, is yiumerically 
equal to the product of the current and the resistance. 

By the above statement, 

pressure = current x resistance, 
or volts = amperes X ohms, 
or E = I X U (28). 

Problem 30. — What pressure is required to cause 10 amperes to flow 
through an electrical appliance if the resistance is 4.5 ohms? 
By Formula (28) E = I x R = 10 x 4.5 = 45 volts. 

Fourth. — The pressure varies directly as the current and re- 
sistance. For example, if a greater current is to be sent through 
the same resistance, a greater pressure must he applied; also, if 
the same current is to be passed through a higher resistance a 
greater pressure must be applied. E = I x R. 

Problem 31. — What pressure is required to cause 15 amperes to flow 
through the device in Problem 30? 

By Formula (28) E = I x R = 15 x 4.5 = 67.5 volts. 

Problem 32. — If the device in Problem 30 had a resistance of 9 ohms, 
what pressure must have been applied to have had 10 amperes flow 
through it? 

By Formula (28) E=IxR = 10x9=90 volts. 

Problems 31 and 32 illustrate how E increases directly with R and I. 
If either R or I had been decreased E would have been decreased also. 

Fifth. ■ — The resistance required to be inserted in any circuity 
so that a given current will flow by reason of a known pressure, 
is equal to the pressure to be applied, divided by the current that 
is to be maintained. 

By the above statement, 

. , pressure 

resistance = , 

current 

volts 
or ohms = 



amperes' 



or - R = I ■ • • (29). 



102 LESSONS IN PRACTICAL ELECTRICITY 

Problem 33. — An electric heater is constructed of No. 18 iron wire and 
is placed across 110 volts. If it takes a current of 10 amperes, what will 
be the value of its hot resistance? 

■p" 1 1 

By Formula (29) R = - =— - = 11 ohms (hot). 

Sixth. — The resistance required for any circuit varies directly 
with the pressure applied, and inversely as the value of the current 
to be maintained. For example, with a constant pressure the 
resistance must be halved if the cmTent is to be doubled; on 
the other hand, with a constant current to be maintained in a 
circuit at double the pressure, the resistance must be doubled. 

Problem 34. — What should be the resistance of an electric heater which 
will take a current of 20 amperes on a 110-volt circuit? 

By Formula (29) R = — = -— ■ =5.5 ohms. 
-^ I 20 

Compare with Problem 33. 

Problem 35. — If the pressure is 220 volts in Problem 33, what resis- 
tance will be required? 

E 220 
By Formula (29) R = - = — - = 22 ohms. 

104. Circuits and their Resistance. — There are two simple 
ways of connecting two or more pieces of electrical apparatus. 
First, when the pieces are connected, as are the coils A and B in 
Fig. 77, they are said to be in series, and the same current (am- 
peres) will flow through each piece of apparatus so connected 

regardless of its resistance. 

..^^mm mH^^—^ ^^^^^^^' ^^^^^ ^^^ P^^^^^ ^^ ap- 
paratus are connected so that 

the total current is divided be- 
tween them, they are said to be 
in parallel with each other, as 
_ . the coils A and B in Fig. 78. 

^°' ^ " Series^^^^ ^^^^^ ^ Midtiple or shunt are other 

names for the connection of 
apparatus in this manner. The ten lamps in Fig. 79 are in 
parallel with each other. 

The two combinations, series and parallel, may exist in the 
same circuit as in Fig. 80, where the parallel combination of 
lamps C and D is in series with the series combination of 



OHM'S LAW 



103 



M/VWWW^— ^ 



Fig. 78. 



Two Resistances in 
Parallel. 



tffiMSM 



Pi 



lamps A and B. Also, there may be a multiple of series com- 
binations, as in Fig. 83, where lamps A and B are in series, 
and then in parallel with the 
series combination of lamps C 'VWWW 

and D; this is termed a mul- 
tiple-series connection. The 
cells of a battery are some- 
times connected in this manner 
ffll23). 
105. Resistances in Series. — 

To FIND THE TOTAL RESISTANCE 
OF A NUMBER OF RESISTANCES 
CONNECTED IN SERIES: 

Find the sum of the resistances connected. If in Fig. 77, A 
equals 40 ohms and B equals 160 ohms, then the total resis- 
tance equals 40 + 160 = 200 
ohms. The same current will 
flow through A as through B. 
106. Equal Resistances in 
Parallel. — Joint Resistance. 
In Fig. 78 the two resistances, 
A and B, are connected in 
parallel, and then to the bat- 
tery. If the resistance of A is equal to that of B, the conduct- 
ance will also be equal and the current will divide, one half 
flowing through A and the other 



half through B. Since the total 
area of the conducting circuit 
has been increased, the com- 
bined or joint resistance of A 
and B will be less than either 
resistance separately. If the 
resistance of A equals that of 
B, then the area will have been 
doubled, and the joint resis- 
tance equal to one half that of 
A or B. Thus, if A and B = 10 ohms each; joint resistance = 
J of 10 or 5 ohms. With three equal resistances in parallel 
the joint resistance will be i the value of one of the resistances. 



Fig. 79. — Ten Incandescent Lamps 
Connected in Parallel to a Generator. 



r— <A) ® 



o 



Fig. 80. — Two Incandescent 
Lamps in Parallel and in Series 
with Two Lamps in Series. 



104 LESSONS IN PRACTICAL ELECTRICITY 

To FIND THE JOINT RESISTANCE OF ANY NUMBER OF 
EQUAL RESISTANCES CONNECTED IN PARALLEL: 

Divide the value of a single resistance by the number connected 
in parallel. 

Let R = a single resistance, 

nq = number of equal resistances in parallel, 
J. R. = joint resistance. 

Then, J. R. = — (30). 

nq , ^ ^ 

To FIND THE NUMBER OF EQUAL RESISTANCES CONNECTED 
IN PARALLEL (nq) WHEN THE JOINT RESISTANCE (J. R.) AND 
THE VALUE OF A SINGLE RESISTANCE (R) ARE KNOWN: 

Divide the value of a single resistance by the joint resistance. 
Thus, nq = j-^ (31). 

To FIND THE VALUE OF A SINGLE RESISTANCE (R) WHEN 
THE JOINT RESISTANCE AND THE NUMBER OF EQUAL RESIS- 
TANCES IN PARALLEL ARE KNOWN: 

Multiply the joint resistance by the number of equal resistances 
connected in parallel. 

R = J. R. X nq (32)o 

Problem 36. — Ten incandescent lamps are connected in parallel (Fig. 
79). Each lamp has a resistance (hot) of 220 ohms. What is the total 
or joint resistance of the lamp circuit ? 

By Formula (30) J. R. = — = ^ = 22 ohms. 
•^ nq 10 

Problem 37. — The joint resistance of 55 lamps connected in parallel is 
4 ohms. What is the resistance of 1 lamp? 

By Formula (32) R = J. R. x nq = 4 x 55 = 220 ohms. 

Problem 38. — The joint resistance of a number of electromagnets con- 
nected in parallel is 8 ohms and the resistance of one magnet is 40 ohms. 
How many magnets are connected ? 

By Formula (31) nq = Tir^ ~^ = ^ electromagnets. / 

J. xv. o ^ 



OHM'S LAW 



105 



resistance, i 



or 1^ mhos. 



107. Conductance of a Circuit. — The conductance of a 
circuit is the reciprocal of its resistance. (The reciprocal of a 
number is the quotient obtained by dividing one by that num- 
ber, as the reciprocal of 4 is i; of | is | = 1^.) The unit of 
conductance is the mho (ohm spelled backward) . A wire of 
1 ohm resistance has a conductance of 1 mho; if of 2 ohms 

mho; 8 ohms resistance, i mho; | ohm resistance, 
The resistance of a circuit is the reciprocal 
of its conductance. A wire of 7 mhos conductance has + ohm 
resistance. 

108. Unequal Resistances in Parallel. — In Fig. 81, two 
unequal resistances are connected in parallel. The joint re- 
sistance will be less than either 
resistance considered separately. 

To FIND THE JOINT RESIS- 
TANCE OF TWO UNEQUAL RESIS- 7 oh 
TANCES CONNECTED IN PARALLEL : ^ /^WV\A/ ^ 

Divide the product of the resis- 
tances hy their sum. 

Let R = first resistance, 

Ri= second resistance, ■ 
J. R.= joint resistance. 



J Ohms 

r-^mm — 1 



Fig. 81. 



Two Unequal Resistances 
in Parallel. 



Then the joint conductance = ^ + ^ 

Ri+R 



and the joint resistance = 
R X Ri 



1 1 _ Ri + R 
~ RxRi 

ohms. 



mhos. 



RxRi 



or 



J. R. 



R + Ri 



(33). 



Problem 39. — • Find the joint resistance of two coils in parallel, having 
a resistance of 3 and 7 ohms respectively (Fig. 81). 

By Formula (33) J. R. = ^^^•= |^ = 2.1 ohms. 

R + Ri o + 7 

If more than two unequal resistances are connected 
IN parallel: 

First find the joint resistance of two resistances, and consider- 
ing this as a single resistance, combine it with a third resistance, 
arid so on. 



106 



LESSONS IN PRACTICAL ELECTRICITY 



109. Conductance Method for Conductors in ParalleL — 

To FIND THE JOINT RESISTANCE OF ANY NUMBER OF RESIS- 
TANCES CONNECTED IN PARALLEL: 

Find the sum of the conductances of the different paths through 
which the current flows and the joint resistance will be the 
reciprocal of the sum thus obtained. 

Problem 40. — Find the joint re- 
sistance of two coils having 3 and 7 
ohms resistance respectively (Fig. 
81) by the conductivity method. 

By ^ 107 joint conductance = 



2 Ohms 

r-Wm ^ 

4 Ohms 



6 Ohms 

"—mm — ' 



117+3 



3-^7 



21 



-mho. 



Joint resistance 



21 
10 



= 2.1 ohms. 



Compare with Problem 39. 



Fig. 82. — Three Unequal Resis- 
tances in Parallel. 



Problem 41. — Find the joint re- 
sistance of three coils of wire having 
resistances of 2, 4, and 8 ohms respectively (Fig. 82). 

T.^..^.. . 1114+2+17, 
By H 107 jomt conductance = - + t + o = o " = o ^^o- 

z 4 o o o 



Joint resistance 



8 



= 1.142 ohms. 



110. Resistances Joined in 
Multiple-series. — When the 

RESISTANCES OF ALL THE SERIES 
GROUPS IN A MULTIPLE-SERIES 
CIRCUIT ARE THE SAME I 

Find the resistance of one 
group, and divide this sum by the 
number of groups in parallel. 



■<&■ 



■<£>■ 



o 



Fig. 83. — Multiple-series Connec- 
tion of Four Incandescent Lamps. 



Let R = resistance of one of like devices (lamp or coil of wire), 
ns = number of devices in series in one group, 
nq = number of groups in parallel. 

R X ns 



Total resistance of multiple-series combinations 



nq 



(34). 



OHM'S LAW 



107 



In Fig. 83, if the resistance R of each lamp is 220 ohms, the 
total resistance of the lamp combination would equal, by 
Formula (34), 220 ohms, since there are two groups and two 
lamps in series in each group. 

When the groups are of unequal resistance: 
Find the sum of the series resistances in each group, and treat- 
ing these as single resistances proceed as in T[ 108 or H 109. 

111. Division of Current in a Divided Circuit. — The division 
of current in the branches of a multiple circuit is directly pro- 
portional to the conductance of the branches, or inversely pro- 
portional to their resistance. 

If A and B, Fig. 78, are equal in resistance and a current of 
12 amperes flows from the battery, 6 amperes will flow through 
A, and 6 amperes through B. 



A- 6 Ohms 

wwwvww 

B-/2 Ohms 

WWWVWVWW 

C-/6 Ohms 

wmNm 



Fig. 84. — Division of Current in the 
Branches of a Multiple Circuit. 



If A has a higher resistance than 
B (and consequently a lower 
conductance), then the greater 39 Amperes 
portion of the current will flow 
through the lower resistance of 
B (which has a higher conduct- 
ance). 

If A has 2 ohms resistance 
and B 1 ohm, then twice as much current will flow through B 
as through A; or the current is divided into three parts, one- 
third of which flows through A and two-thirds through B. If 
the total current is 12 amperes, A then receives 4 amperes and 
B 8 amperes. 

Problem 42. — A current of 39 amperes is passed through three coils of 
wire joined in multiple, Fig. 84, having the following resistances: A = 8, 
B = 12, and C = 16 ohms. How many amperes will each coil receive? 

The conductance of A is - =7- mho, of B is — = — - mho, and of C is — - 
8 48 12 48 ' 16 

= |mho. 

By 1[ 109 their joint conductance = -+ Tt; + 77 = 73 = js mho. 

o U Id 48 48 

Consider the current to divide into 13 parts (6+4+3), 6 parts of 
which pass through A, 4 through B, and 3 through C, or directly as their 
conductances. Then the currents through the various coils are 



108 LESSONS IN PRACTICAL ELECTRICITY 

A = — of 39 =18 amperes; 
lo 

4 
B= — of 39 = 12 amperes; 

lo 

3 
C = — of 39 = 9 amperes. 

lo 

Total current = 39 amperes. 

112. Ohm's Law Applied to a Battery Circuit. — When 
the total E, M. F, is used in Ohni's Law, the total resistance of 
the circuit must also he used in calculating the current strength. 
For example, when an electromagnet of 0.4 ohm is connected 
to a cell of 2 volts E. M. F. the current through the spool 
will not be E -^ R or 2 -=- 0.4 = 5 amperes, as might at first be 
supposed. It requires a certain portion of the 2 volts to cause 
the current to flow through the cell's internal resistance. The 
internal resistance must he added to the external resistance to 
ohtain the total resistance of the circuit, which total resistance is to 
he divided into the total pressure to ohtain the current strength. If 
the internal resistance of the above cell is 0.6 ohm, then the 
total resistance is 0.4 + 0.6 = 1 ohm, and the current equals 
E^R=2^1=2 amperes, or less than one-half of the former 
value. 

Let R = total external resistance of the circuit in ohms, 
r = internal resistance of the battery in ohms. 
Then R + r = total resistance of the circuit (external + inter- 
nal), and Ohm's Law becomes, 

1=^ ........ .(35). 

where r represents the internal resistance, in ohms, either of 
a cell or of the windings of a generator. 

Problem 43. — If a bichromate cell, E. M. F. = 2 volts, internal resis- 
tance = 0.5 ohm, is connected to a.n electromagnet having a resistance of 
1.5 ohms, what current will the magnet receive? 
T? 2 

By Formula (35) I = :5 = , - , ^ ^ - 1 ampere. 

xv -(- r 1.0 + u.o 

Ohm's Law applies equally as well to any part of a circuit as 
to the whole circuit. When applied to part of a circuit, care 



OHM'S LAW 109 

must be exercised to use the value of the pressure applied to the 
resistance of that portion of the circuit considered, when E will 
still represent the volts applied and R the resistance of the part 
of the. circuit to which E is apphed. When E is used as the 
total pressure, R, to correspond, must be the total resistance. 
When E is used as the pressure applied to part of a circuit, 
R must be the resistance of that part to which this pressure is 
applied. This double application of the law is illustrated in 
Problems 43 to 46, which should be carefully studied. 

Problem 44. — The E. M. F. of a cell is 2 volts, its internal resistance 
is 0.5 ohm. Several different resistance spools are joined in series and 
connected to the cell. By electrical measurement it is found that the 
pressure causing the current to flow through a 0.4 ohm spool is 0.6 volt. 
What is the value of the current flowing through this spool? Make a 
sketch of the circuit. 

By Formula (27) 1=—=-— = 1.5 amperes. 

K, 0.4 

Since the current is the same in all parts of a series circuit, 
1.5 amperes must flow through each of the other spools men- 
tioned; also through the internal resistance of the cell. This 
problem illustrates the difference between E. M. F. and poten- 
tial difference, see H 35. The difference of potential, or pres- 
sure between the spool terminals, is 0.6 volt, while the E. M. F. 
is 2 volts. In Ohm's Law E may represent either value. See 
Lesson X. 

Problem 45. — What portion of the total E. M. F. in Problem 44 is 
used in overcoming the internal resistance of the cell ? 

By Formula (28) E = I x R, from which is derived 

E=Ixr (36). 

This gives the pressure lost or volts drop inside the cell, ^ 131. 
By Formula (36) E = I x r = 1.5 x 0.5 = 0.75 volt. 

Problem 46. — What portion of the E. M. F. is available for the other 
spools in the series circuit of Problems 44 and 45 ? 

E 2 
By Formula (29) total resistance = r- = —- = 1.333 ohms. 

1 1.5 

Resistance of cell (0.5) plus resistance of one spool (0.4) = 0.9 ohm. 
1.333 - 0.9 = 0.433 ohm for balance of spools. 

By Formula (28) E=IxR=1.5x 0.433 = 0.6495 volt. 



no LESSONS IN PRACTICAL ELECTRICITY 

E 
Using Formula (35), 1= , we may also change Formulae (28) and 

(29) to include the internal resistance, by replacing R by R + r, thus: 

E=Ix(R+r) .(37). 

E 

and (R + r) = - ; 

■p 
by transposition R = Y-r...... (38). 

E 
Also r=--R. ... (39). 

Problem 47. — A cell with an internal resistance of 2 ohms sends a 
current of 0.035 ampere through the electromagnets of a bell having a 
resistance of 48 ohms. What is the E. M. F. of this cell ? 

By Formula (37) E = I x (R + r) = 0.035 x (48 + 2) = 0.035 x 50 
= 1.75 volts. 

Problem 48. — A current of 0.25 ampere is maintained through a circuit 
by an E. M. F. of 2 volts; the internal resistance of the cell is 0.5 ohm. 
What is the value of the external resistance? 

By Formula (38) R = y - r = -^ - 0.5 = 7.5 ohms. 



QUESTIONS 

1. An electromagnet connected to a Leclanche cell attracts many 
more fihngs than when it is connected to a Daniell cell. Why ? 

2. Upon what factors do the E. M. F.'s of batteries and generators de- 
pend ? 

3. An incandescent lamp receives insufficient current to properly 
illuminate it. Why is this, and what is necessary in order that it may 
operate at its proper candle-power ? 

4. Explain Ohm's Law. 

5. With a constant resistance, how will the current strength vary 
with the E. M. F.? 

6. With a constant pressure how will the current vary with the re- 
sistance ? 

7. The arc lamps connected to a series generator are joined in series 
with it. How is the resistance of the circuit affected as additional lamps 
are inserted in the circuit ? 

8. A number of incandescent lamps are connected in multiple to a 
generator. How will the resistance of the circuit be affected if one lamp is 
turned off ? 

9. What do you understand by the term conductance? 



OHM'S LAW 111 

10. An electric heater consists of coils of iron wire through which a 
current of 2.5 amperes flows, when joined in parallel with an incan- 
descent lamp which receives 1 ampere. Which object possesses the higher 
resistance ? Give proof for answer. 



PROBLEMS 

1. What pressure must be applied to an incandescent lamp if it has 
a resistance of 55 ohms and requires 2.2 amperes ? Ans. 121 volts. 

2. A Daniell ceU has an E. M. F. of 1 volt and an internal resistance 
of 2.2 ohms. What current will flow through an electromagnet con- 
nected to it, wound with 150 feet of No. 18 B. & S. copper wire? Ans. 
0.312 ampere. 

3. Four hundred incandescent lamps are connected in parallel to a 
generator circuit. Resistance of the Une is 0.5 ohm and the hot resistance 
of one lamp is 220 ohms. Potential difference at the generator terminals 
is 112 volts. What current flows through the circuit? Give a sketch. 
Ans. 106.66 amperes. 

4. What length of No. 24 B. & S. copper wire would have an equivalent 
resistance to the joint resistance of 2 lamps connected in parallel? One 
lamp has a resistance of 110 ohms, the other 33 ohms. Ans. 950 feet. 

5. Three copper electroplating baths are connected in parallel to a 
generator which furnishes 117 amperes to them. The resistance of the 
baths are: No. 1, 24 ohms; No. 2, 36 ohms; No. 3, 48 ohms. What cur- 
rent does each bath receive ? Give sketch. Ans. 54; 36; 27 amperes. 

6. Sketch and name six combinations of 4 incandescent lamps con- 
nected to a pair of supply lines. Each lamp has a resistance of 220 ohms 
(assumed constant) and the potential across the mains is 110 volts. What 
current will each combination receive? Ans. 0.125; 2; 0.5; 0.2; 0.376; 
0.3 amperes. 

7. In a trolley car, five lamps, each requiring ^ ampere and 100 volts, 
are connected in series between the line and track across which 500 volts 
potential is maintained. If 10 cars wired as above were using lamps 
what would be the joint resistance of the lamp circuit and how much 
current would flow from the power station ? Ans. 100 ohms; 5 amperes. 

8. The current through the field magnets of a dynamo is 2 amperes 
and the applied pressure 120 volts. What is the resistance of the field 
magnets ? Ans. 60 ohms. 

9. The E. M. F. of a cell is 2.44 volts, its internal resistance 0.6 ohm, 
and it is connected to a circuit of 1.4 ohms. What pressure is required 
to send the current used through the battery ? Ans. 0.732 volt. 



LESSON IX 
SERIES AND PARALLEL BATTERY CONNECTIONS 

Methods of Varying Current Strength — The Size of a Cell — Cells 
Connected in Series to Increase the E. M. F. — Cells Connected in 
Parallel or Multiple for Quantity — The Internal Resistance of Cells 
in Series — Curreiit from Cells in Series — The Internal Resistance 
of Cells in Parallel or Multiple — Current from Cells in Parallel or 
Multiple — Advantage of Parallel Connection — Advantage of 
Series Connection — Cells Grouped in Multiple-series — Internal Re- 
sistance of Multiple-series Combination of Cells — Current Strength 
from any Combination of Cells — Cells in Opposition — Questions and 
Problems. 

113. Methods of Varying Current Strength. — By Ohm's 
Law, I = E -^ R, the current through any circuit may be in- 
creased in two ways, namely : by increasing the pressure, E (the 
dividend), or by decreasing the resistance, R (the divisor); 
by decreasing the pressure, or increasing the resistance, the* 
current will be decreased. For example,- 25 volts will cause 5 
amperes to flow through 5 ohms. If the pressure is raised to 
35 volts the current strength will be 7 amperes. Current from 
any cell may be decreased by inserting resistance in the cell 
circuit. If sufficient current, however, cannot be obtained 
from a cell, and as the E. M. F. is a fixed quantity for each 
type of cell, the E. M. F. may be increased by joining two 
or more cells in series, so that the total E. M. F. is the sum 
of the E. M. F.'s of the separate cells. This will be better 
understood from the hydraulic analogies in If 115. 

114. The Size of a Cell. — It has been stated that the 
E. M. F. of a cell is the same for cells of the same type without 
regard to size, but that the current depends on the size. In 
Fig. 85 the cyhndrical tank A has a capacity of 100 gallons 
of water under a pressure of 10 pounds per square inch, due 
to the weight of the piston. Neglecting the weight of the water, 
the pressure gauge will record a pressure of 10 pounds. When 
the valve is opened the water will be discharged at the rate 
of, say, one gallon per minute, under a pressure of 10 pounds 

112 



BATTERY CONNECTIONS 



113 



per square inch, so that at this rate it will require 100 minutes 
to empty the tank. A similar tank B has a capacity of 
10 gallons of water under a pressure of 10 pounds per square 
inch, due to the piston. Neglecting the weight of the water, 



100 Oollon Tank 



10 Gallon Tank 



10 lbs. per 
Square Inch 




(Tank A E 



Valve 

Fig. 85. - 



Pressure ' 
Oauge 

Two Cylindrical Tanks of Different Capacities, 
Containing Water under Pressure. 



the pressure gauge will record 10 pounds also. The diameter 
of the pipe is the same size as for tank A, and when this valve 
is opened the water will flow out at the rate of one gallon per 
minute under a pressure of 10 pounds per square inch as be- 



Swifch 



..Switch 



Zinc-: 




m... 




Galvanometer 
^-Carbon Zinc 

"^; — Chromic Acid 



10 Ampere Hour Cell , 
Cell B 
100 Ampere Hour Cell 
Cell A 
Fig. 86. — Two Cells of Different Size but Having the Same E.M.R 

fore, thus requiring only ten minutes to empty tank B. ' In 
both tanks the pressure and the rate of flow are the same, but 
tank A will maintain the current of water ten times as long as 
tank B. 

Now consider Fig. 86, in which the large cell A has a 
capacity of 100 ampere-hours (see \ 94) and an E. M. F. of 



114 LESSONS IN PRACTICAL ELECTRICITY 

2 volts. When the switch is closed the galvanometer indicates, 
say, 45 divisions deflection, corresponding to a current strength 
of one ampere, and sufficient chemicals and zinc are present 
to maintain this current for 100 hours when the pressure is 
2 volts and the rate of flow one ampere. Consider now a 
similar small cell B, which has a capacity of 10 ampere-hours 
and an E. M. F. of 2 volts. When the switch is closed through 
the same galvanometer the deflection is 45, as before, corre- 
sponding to a current strength of one ampere, sufficient chemi- 
cals and zinc being present to maintain this current for only 
10 hours when the pressure is 2 volts and the rate of flow one 
ampere (neglecting the internal resistance) . Thus the quantity 
of electricity depends on the size of the cell. If a large drain 
pipe had been used in tanks A and B, they would have been 
emptied more rapidly since the rate of flow would have been 
greater. If a galvanometer wound with a larger wire had 
been used, the cells A and B w^ould not have maintained the 
current for so long a time, the rate of flow, however, being 
greater. 

115. Cells Connected in Series to Increase the E. M. F. — 
Consider the hydraulic analogy in Fig. 87, where the two 
similar cylindrical tanks A and B have a capacity of 100 gal- 
lons each. The pressure on the water in tank A and con- 
necting pipe is 10 pounds per square inch, due to the weight 
of the piston, so that the pressure gauge 1 indicates 10 pounds 
per square inch. In tank B the pressure on the water is 10 
pounds per square inch, due to the pressure of the piston on 
tank A above it, plus 10 pounds per square inch, due to the 
weight of its own piston, so that gauge 2 wifl register 20 pounds 
per square inch. The weight of the water is neglected. When 
the valve in the drain pipe of tank B is opened this tank will 
dehver the same quantity of water (100 gallons) as would be 
delivered by tank B, but at double the pressure. The rate 
of flow is, therefore, twice as rapid. If a number of similar 
tanks were connected in like manner above A, the pressure 
on gauge 2 would be increased 10 pounds per square inch for 
each tank added, although the quantity of water delivered 
through the valve would be the same as that of one tank. 
Consider now Fig. 88, where two cells, each having a capacity 



BATTERY CONNECTIONS 



115 



10 lbs. per 
Square Inch 



of 100 ampere-hours and an E. M. F. of 2 volts, are joined 
in series so that the E. M. F/s are in the same direction. 
The carbon pole of the first 
cell is connected to the zinc 
pole of the second cell, and 
the two remaining terminals 
connected to the galvanom- 
eter. Cells connected in this 
manner are joined in series. 
The total pressure applied to 
the galvanometer when the 
switch is closed is twice the 
pressure of one cell (neglect- 
ing internal resistance), or 4 
volts. The total quantity 
of electricity that will pass 
through the galvanometer is 
the same as would be de- 




Pressure Oauge 



10 lbs. per 
Square Inch 



Pressure Gauge 2 



Galvanometer 
Cu 



, „ Fig. 87. — Two Cylindrical Tanks, 

livered by each cell sepa- Full of Water, Connected in Series for 
rately, 100 ampere-hours, al- Pressure. 

though, since it is delivered Gauge 2 records twice the pressure indi- 

, ^ . , , „ cated upon gauge 1. 

at twice the pressure of a 

single cell, the rate of flow is twice as great as with one cell. 

- When a number of 

similar cells are thus 

connected in series the 

pressure applied to the 

galvanometer will be 

increased by 2 volts 

for each cell so added, 

but the total quantity 

of electricity that can 

be delivered will be 

equal to the capacity 

of only one cell. 

116. Cells Connected in Parallel or Multiple for Quantity. — 

In Fig. 89 two similar cylindrical tanks have a capacity of 100 

gallons of water each, and are connected by a pipe, C, to which 

a pressure gauge is attached. The piston in each tank exerts 




100 Annpere Hour 



2 Volts 



100 Ampere Hour 
> 
2 Volts 



Fig. 88. — Two Cells Connected in Series for 
Pressure. 

The galvanometer indicates twice the pressure of one cell. 



116 



LESSONS IN PRACTICAL ELECTRICITY 



a pressure of 10 pounds per square inch, and the pressure 
gauge records only 10 pounds pressure, the same as though 
only one tank were used. The addition of any number of 
similar tanks will not increase the pressure, which will always 
remain 10 pounds per square inch. The weight of water is 
neglected. Although the pressure is not increased, the quan- 
tity of water which can be drawn from the valve in the drain 
pipe increases in proportion to the number of tanks so added; 
thus, the total capacity of 2 tanks is 200 gallons; 6 tanks, 600 
gallons. In Fig. 87 the tanks were arranged in series to add 



Tank A 
■100 Gallons 



10 lbs. per 
Square Inch 



TankB r<J 
100 Oollons 



== Wafer 



10 lbs per 
Square Inch 



Water 



^ d±»'--\/ali^e 



w 



■essure Gauge 



Fig. 89. — Two Cylindrical Tanks, Full of Water, Connected in 
Parallel for Quantity. 

The pressure gauge records the pressure due to only one tank, but the 
quantity of water delivered is equal to the sum of the two capacities. 

their pressures together, while in this case the tanks are ar- 
ranged in parallel to add their volumes together. 

In a voltaic cell, the output depends upon the amount of 
zinc to .be acted upon. Suppose the cell gives 1 ampere-hour 
for each square inch of zinc that is exposed to the acid, then 
by increasing the area of the zinc plates a greater quantity of 
electricity can be obtained from the cell. This can be done in 
two ways: by making one very large cell, 8.s B, Fig. 90, or by 
connecting the like plates of two or more smaller cells, as in 
A, Fig. 90. Here the zinc plates of two cells are connected by 
a wire, forming one large zinc plate with double the area, 
the copper plates being similarly connected. Cells so connected 
are arranged in parallel or multiple. When the switch is closed' 
in arrangement A the galvanometer is subjected to 2 volts 
pressure, neglecting internal resistance, which pressure would 



BATTERY CONNECTIONS 



117 



not be increased, no matter how many cells were thus con- 
nected. The total quantity of electricity that will flow through 
the galvanometer will increase in proportion to the number of 
cells so added. The two cells in A, therefore, could maintain 
1 ampere through the galvanometer for 200 hours at a pressure 
of 2 volts, as could also the larger cell B. The advantage, 
then, of having small cells is that they can be arranged either 
for pressure or quantity, as may be desired, by connecting them 
in series or in multiple. 



<-2 Volts— 



Zn- 



Zrr- 




Zn-i, 


y 


Cu -. 


J^ 












f 


i 


Y 




ll 


P 



tOOAmpereHour 
x.— 2Vo!ts—- 



f 



"-<3} 



200 Ampere Hoar 

= r 



'^Swifch 



Galvanometer 



■ Switch 



Oalvanometer 
Fig. 90. — Two Cells Connected in Parallel for Quantity. 

The total capacity and E. M. F. of the two small cells are exactly equal to the 
corresponding quantities of the larger cell. 

Experiment 47. — Using a galvanometer of high resistance, compare 
the E. M. F.'s of different types of cells and record the deflections, the 
value of which will vary as the E. M. F. varies. 

Experiment 48. — Connect unlike poles of two similar cells (which is 
termed joining cells in series) and attach the two remaining terminals 
to a high-resistance galvanometer. The deflection is greater than with 
one cell, because the E. M. F.'s of the cells have been added together 
and a greater pressure is applied to the galvanometer circuit. If the de- 
flections are directly proportional to the current, the value will be nearly 
doubled. With three similar cells in series the pressure is increased three- 
fold, and so on. 

Experiment 49. — Connect two dissimilar cells in series (for example a 
Daniell cell, 1.1 volts, and Leclanche cell, 1.5 volts) with a high-resistance 
galvanometer, and the deflection is greater than with either cell alone. 
The pressure applied to the galvanometer is equal to the sum of the two 
pressures in series (1.1 + 1.5 = 2,6 volts). 



118 LESSONS IN PRACTICAL ELECTRICITY 

Experiment 50. — Record the deflection produced by one cell (say a 
Daniell) connected to a high-resistance galvanometer. Using two similar 
cells, connect the positive poles by one wire, and the negative poles by 
another wire, and attach lead wires from these junctions to the galva- 
nometer (when hke poles are thus connected the cells are joined in parallel 
or multiple). The deflection is not perceptibly greater than with one 
cell, because the E. M. F. of two or more simflar cells, joined in parallel, 
is the same as the E. M. F. of one cell; hence, two Daniell cefls of 1 volt 
each joined in parallel will have a total E. M. F. of 1 volt; 10 such cells 
in parallel will have a total E. M. F. of 1 volt; 10 such cells in series will 
have a total E. M. F. of 10 volts. In the above experiments a galvanom- 
eter of many turns of fine wire is used, so that little current will flow 
from the cells, and the deflections represent nearly the true pressures. 

117. The Internal Resistance of Cells in Series. — When 
a number of cells are connected in series, and to an external 
circuit, the current flowing through the external circuit must 




Fig. 91. — Eight Cells Connected in Series for Pressure. 

The pressure is eight times that of one cell, as it also the internal resistance. 

pass through each cell so connected (Fig. 91), requiring, there- 
fore, a certain fraction of the total E. M. F. to overcome the 
resistance of each cell. 

To FIND THE TOTAL INTERNAL RESISTANCE OF A NUMBER 
OF SIMILAR CELLS CONNECTED IN SERIES: 

Multiply the resistance of one cell by the number so connected. 

Let r = internal resistance of one cell, 
ns = number of cells in series. 
Then 

total internal resistance of cells in series = r x ns (40). 

Problem 49. — Ten Daniell cells, with an internal resistance of 2 ohms 
each, are connected in series. What is the total internal resistance? 
By Formula (40) total resistance = r x ns = 2 x 10 = 20 ohms. 



BATTERY CONNECTIONS 119 

118. Current from Cells in Series. — To find the cukrent 

THAT WILL BE MAINTAINED IN AN EXTERNAL CIRCUIT BY A 
NUMBER OF CELLS IN SERIES I 

Find the total E. M. F. applied by multiplying the E. M. F. of 
one cell by the number connected in series. Find the total internal 
resistance by Formula (4-0). Then by Ohm^s Law the current 
equals the total E. M. F. -=- the total resistance. 
Let E = E. M. F. of one cell, 

r = internal resistance of one cell, 
ns = number of cells in series, 
R = external resistance. 
Then 

I. Exns 

(r X ns) + R 

Problem 50. — Ten Daniell cells are joined in series to two spools of 

wire in series, one 4 ohms, the other 6 ohms. E. M. F. of each ceU is 1 volt, 

and the internal resistance of each cell is 2 ohms. What current will flow 

through the circuit ? 

T. ^? 1 /.1^ T E xns 1 XIO 10 1 

By Formula (41) I = ^ = 7- — —■ = tzz^ = ~ ampere, 

^ ^ ^ (r X ns) + R (2 X 10) + 10 30 3 ^ ' 

where R = 6 + 4 = 10 ohms. 

119. The Internal Resistance of Cells in Parallel or 
Multiple. — When a number of similar cells are connected in 
multiple (Fig. 92), and to an external circuit, the total current 




Fig. 92. — Eight Cells Connected in Parallel for Quantity. 

The pressure is the same as that of one cell; the total internal resis- 
tance is one-eighth of that of one cell; the current is nearly eight times 
that of one cell. 

flowing through the external circuit does not pass through 
the resistance of each cell, as in the series case, but is divided 
among the cells in proportion to the number in parallel. The 
internal path for the total current is of much lower resistance 
than the resistance of one cell. Cells connected in parallel 
have their like plates connected. Fig. 92, forming practically 



120 LESSONS IN PRACTICAL ELECTRICITY 

one large cell, the positive and negative plates of which are 
equal in area to the sum of the areas of the respective plates 
in the separate cells. The area of the conducting liquid is 
proportionately increased, and consequently, the internal resis- 
tance decreased. (See If 72.) 

To FIND THE INTERNAL RESISTANCE OF A NUMBER OF 

CELLS IN parallel: 

Divide the resistance of one cell by the number connected in 
parallel. 

Let r = internal resistance of one cell, 

nq = number of cells in multiple or parallel. 
Then 

total internal resistance of cells in parallel = — • • ■ (42). 

nq 

Problem 51. — The cells of Problem 50 are joined in parallel. What is 
the internal resistance ? 

r 2 1 

By Formula (42) total internal resistance = — = — = - ohm. 

nq 10 5 

Experiment 51. — Connect a very large Daniell cell to a low-resistance 
galvanometer and record the deflection (say 60 divisions). Now join a 
much smaller similar cell to the same galvanometer and the deflection is 
much less (say 20). The pressure is the same in both cases, but the inter- 
nal resistance of the small cell is higher, and since I = E -^ (R + r), For- 
mula (35), the current and the deflection must be less. Connect three of 
the smaller cells in parallel. Fig. 92, and to the galvanometer, and the 
deflection is now equivalent to that of the single large cell. The pressure 
is no higher since the cells are in parallel, therefore the total internal 
resistance of the three cells must be equal to that of the one large cell, 
since the current and pressure are the same. 

120. Current from Cells in Parallel or Multiple. — To find 

THE CURRENT THAT WILL BE MAINTAINED IN A CIRCUIT BY 
A NUMBER OF SIMILAR CELLS JOINED IN PARALLEL! 

Find the total internal resistance of the cells in -parallel by 
Formula (4^). Divide the E. M. F. of one cell by the sum of 
the external and internal resistances of the circuit. 
Let E = E. M. F. of one cell, 

r = internal resistance of one cell, 
R = total external resistance. 



BATTERY CONNECTIONS 121 

Then — = total internal resistance of the cells in parallel, and 
nq 

the current, according to Ohm's Law, is 

1=-^- (43). 

nq 

Problem 52. — Ten Daniell cells are joined in parallel and to an exter- 
nal resistance of 10 ohms. E. M. F, of each cell is 1 volt. Internal resis- 
tance of each cell is 2 ohms. Find the current through the external circuit. 

F 1 
By Formula (43) I = = = 0.09 ampere. 

- + R - + 10 
nq 10 

By comparison with Problem 50, it will be noted that with this par- 
ticular external resistance the series arrangement of the cells is much 
better, as nearly four times the current flows through the circuit when 
the cells are in series as when connected in multiple. 

121. Advantage of Parallel Connection. — Cells are con- 
nected in parallel when it is desired to obtain the maximum 
current through a low external resistance circuit, or when a 
small current is required for a long period of time. When so 
grouped the cells are equivalent to one very large cell, and 
are arranged to give a large quantity of electricity. When 
connected to a low external resistance, as compared with the 
internal resistance, the strength of current will also be large, 
while with a high external resistance the current will be small. 
The total quantity of electricity available from the supply of 
the chemicals can thus be used rapidly or slowly, as the con- 
ditions may demand. The following problems will illustrate 
these facts: 

Problem 53. — What current will flow through a resistance of 0.1 ohm 

from a Leclanche or dry cell of 1.4 volts E. M. F. and an internal resistance 

of 0.4 ohm ? 

E 1.4 
By Formula (35) I = ~ = — — = 2.8 amperes. 

Problem 54. — What will be the current in Problem 53 with ten such 
cells in parallel ? 

F 14 14- 

By Formula (43) I = = r-— = ' = 10 amperes. 

— + R 177+0.1 '^ "^ 
nq 10 



122 LESSONS IN PRACTICAL ELECTRICITY 

Problem 55. — Suppose the ten cells in Problem 54 are connected in 
series. What current will flow through the circuit ? 

Ti T^ ^ ,A■,^-T E X ns 1.4x10 14 „ ,, 

By Formula (41) 1= -— — = -— — — -—= —-=3.41 amperes. 

(r X ns) + R 0.4 x 10 + 0.1 4.1 ^ 

The parallel grouping is therefore preferable in the above problems 
if the greatest possible current strength is desired in the external circuit. 

122. Advantage of Series Connection. — A series grouping 
is employed when the external resistance is the principal one 
to be overcome and the maximum current strength is desired 
in the circuit. The advantage of this method will be shown 
by the following problems: 

Problem 56. — A Leclanch4 cell, 1.4 volts and internal resistance of 
0.4 ohm, is connected to an external resistance of 100 ohms. What cur- 
rent will flow through the circuit ? 

By Formula (35) I = ^^ = ^^- = ^ = 0.01394 ampere. 

Problem 57. — Connect ten ceHs similar to that of Problem 56 in 
parallel and find the current. 

By Formula (43) I = ^ ^ = ^^'^ = j^~ = 0.01399 ampere. 

— +R 777+ 100 
nq 10 

Ten cells so connected to this external resistance are, therefore, not 
much better than one cell. 

Problem 58. — Connect the cells of Problem 57 in series and find the 
current strength. 

T. T. 1 /.1^ T E xns 1.4 x 10 14 ^^^^ 

By Formula (41) I = ^^ ^ ^^^^ ^ ,, = (0.4 x 10) + 100 = 104 =''''' 
ampere. 

With the cells in series, nearly ten times the current is passed through 
this resistance as when the cells are connected in parallel. In ][ 121 the 
multiple combination proved to be best adapted for a particular circuit, 
while in this case the series grouping is desirable. The student should 
make a thorough comparison of the problems in ^^ 121 and 122. 

123. Cells Grouped in Multiple-series. — A combination 
of the series and multiple grouping of cells is sometimes de- 
sirable when a number of cells are available, to give either 
the maximum current through an external resistance, or to in- 
crease the capacity of the cells for maintaining a current in a 
circuit for a long period of time. For example, 8 volts E. M. F. 
is required to light q, small lamp, and 8 cells are available, 



BATTERY CONNECTIONS 



123 



with an E. M. F. of 2 volts each. Arrange one group of 4 
cells in series, which will give the desired E. M. F. of 8 volts.^ 
Suppose this group would 
illuminate the lamp for 
4 hours. Arrange a second 



fiMWMJh 



^fcpmv 



Fig. 93. 



Multiple-series Grouping of 
Cells. 

Four cells in series, two groups in parallel. Total 
E. M. F. equals that of one group; total internal 
resistance equals one half of that of one group. 



group of 4 cells in series 
and join this group in mul- 
tiple with the first group 
as in Fig. 93. The total 
E. M. F. is still 8 volts, 
but with two groups in 
parallel the quantity of 
electricity available has 
been doubled, so that the 
lamp will now operate for 
8 hours. Such a grouping of cells is called a multiple-series 
combination (practically a multiple of series groups) . If there 
were two cells, each having an E. M. F. of 8 volts and an inter- 
nal resistance of four times one of the above cells, these two 
could be placed in multiple and substituted for the 8 cells. 

To FIND THE CURRENT FROM A MULTIPLE-SERIES ARRANGE- 
MENT OF CELLS JOINED TO AN EXTERNAL RESISTANCE: 

Compute the E. M. F. and internal resistance of one group of 
cells and consider the results as the data for one ''equivalent'^ 
cell. Then make calculations for the number of such cells 
(groups) arranged in parallel. See *S 125. 

124. Internal Resistance of Multiple-series Combination 
of Cells.— 

To FIND THE INTERNAL RESISTANCE OF ANY MULTIPLE- 
SERIES COMBINATION OF CELLS: 

Multiply the resistance of one cell by the number of cells in one 
group and divide the product by the number of groups in multiple. 
The number of cells in each group must be the same, Fig. 93. 
Let r = resistance of one cell, 

ns = number of cells in series in one group, 
nq = number of groups in parallel. 

1 Neglecting the internal resistance. 



124 LESSONS IN PRACTICAL ELECTRICITY 

Total internal resistance of the combination of cells = 
r X ns 



nq 



(44). 



Problem 59. — Find the internal resistance of a combination of 24 cells 

arranged 6 in series, 4 groups in multiple. Each cell has a resistance of 

2 ohms. 

r X ns 2x6 

By Formula (44) Total resistance = = — - — = 3 ohms. 

•^ nq 4 

125. Current Strength from Any Combination of Cells. — 

To FIND THE CURRENT THAT WILL BE MAINTAINED IN AN 
EXTERNAL CIRCUIT BY ANY MULTIPLE-SERIES COMBINATION 

OF CELLS (Fig. 93): 

Divide the total E. M. F. of one series group by the sum of the 
combined internal and external resistances. 
Let I = current in external circuit, 
E = E. M. F. of one cell, 
ns = number of cells in series in one group, 
nq = number of groups in parallel, 
r = internal resistance of one cell, 
R = external resistance. 

Then by Ohm's Law, Formulae (41) and (44), the current is 

I = -^^^^ (45). 

ns_><_r^j^ 

nq 

Problem 60. — Find the current that would flow through an electrical 
device whose resistance is 2 ohms, when connected to 24 cells arranged 4 
in series and 6 in parallel. Each cell has an E. M. F. of 2 volts and an 
internal resistance of 3 ohms. 

E = 2 volts, ns = 4 cells in one group, r = 3 ohms, nq = 6 groups 
in parallel, R = 2 ohms. 

r> 17 1 Mr^ T E xns. 2 x4 8 ^ 

By Formula (45) I = = t = 7 = ^ amperes. 

n^X_r__^j^ 1^+2 ^ 
nq b 

To FIND THE CURRENT THAT WILL BE MAINTAINED IN AN 
EXTERNAL CIRCUIT FROM ANY SERIES-MULTIPLE COMBINATION 

OF CELLS (Fig. 94): 



BATTERY CONNECTIONS 



125 



Find the internal resistance of one multiple group by Formula 
{42), and consider the re- 
sult as the data for one 
"equivalent' cell {group). 
Calculate the total E. M. F. 
and resistance for the mul- 
tiple groups in series and 
determine the current by 
Ohm's Law. 

Problem 61. — A series-mul- 
tiple combination of 8 cells is 
joined to an external resistance 
of 3 ohms. The cells are ar- 
ranged 4 in parallel, 2 groups 
in series (Fig. 94). Each cell 
has an E. M. F. of 2 volts and 
an internal resistance of 0.5 ohm 
external circuit ? 

E. M. F. of 1 group = 2 volts. 




Fig. 94. — Series-multiple Grouping of 
Cells. 

Four cells in parallel, two groups in series; 
equivalent to two cells in series and four groups 
in parallel. 



What current will flow through the 



E. M. F. of 2 groups in series =2x2=4 volts 
By Formula (42) 



r 0.5 

internal resistance of 1 group =—=-]-= 0.125 ohm. 

nq 4 



By Formula (40) internal resistance of 2 groups in series = r x ns = 



0.125 X 2 = 0.25 ohm. 
By Formula (35) I 



R + r 3 + 0.25 



= 1.23 amperes. 



126. Cells in Opposition. — When two cells are joined in 
parallel their E. M. F.'s are in opposition, since each one tends 
to send a current through the other. If the E. M. F.'s are 
equal no current will flow through the connecting wires. Two 
equal forces, acting in direct opposition, produce equilibrium; 
if, however, the forces are unequal, then motion is produced 
in the direction of the greater force. For example, if the 
pressure acting downward on each piston in tanks A and B, 
Fig. 89, is the same, no water will flow through the connecting 
pipe. Suppose the total downward pressure on A is 10 pounds 
per square inch and on B 30 pounds per square inch, then a 
current of water will flow from B to A, due to the difference 
in pressure between the opposing forces, 30 - 10 = 20 pounds 
per square inch. The piston at A will move upward. When 



126 LESSONS IN PRACTICAL ELECTRICITY 

two cells of unequal E. M. F.'s are connected in opposition 
a current will flow through the connecting wires and internal 
resistance in the direction dictated by the higher E. M. F. 

To FIND THE CURRENT IN ANY CIRCUIT WHEN THE E. M. 

F.'s ARE IN opposition: 

Divide the difference between the E. M. F.^s by the sum of the 
external and internal resistances. 

The opposing E. M. F. is called the Counter E. M. F. and is 

E 

usually represented by ^. Formula (35), I = , may in- 

R + r 

elude the above statement when expressed thus: 

I E - <g 
^ R + r ' 

Problem 62. — Four Daniell cells, each having an E. M. F. of 1 volt and 
an internal resistance of 1.2 ohms, are connected in series and in oppo- 
sition to an accumulator having an E. M. F. of 2 volts and an internal 
resistance of 0.05 ohm. The resistance of the connecting wire is 0.2 
ohm. What is the charging current ? 

E. M. F. = 1 X 4 = 4 volts, <g = 2 volts, r = 1.2 x 4 + 0.05 = 4.85 ohms, 
R = 0.2 ohm. 

"P _ (T A. _ O 

By above Formula I = — = — — j—- = 0.4 ampere. 



QUESTIONS 

1. According to Ohm's Law how may the current through any circuit 
be regulated ? 

2. What is the advantage of a large cell over a small one of the same 
type? 

3. If you were given the choice of two small Daniell cells or one large 
Daniell cell of twice the capacity of the small ones, which would you 
prefer ? Why ? 

4. Why are cells connected in series ? 

5. Why are cells connected in parallel ? 

6. How would the resistance of a battery having four cells connected 
in series, compare with the resistance of the battery if the four cells were 
connected in parallel ? 

7. What is the advantage of a series connection of cells ? What is the 
advantage of a parallel connection of cells ? 



BATTERY CONNECTIONS 127 

8. What advantage is there in grouping a number of cells in a multiple- 
series connection ? 

9. Would you connect two cells having an E. M. F. of 0.7 and 2.4 
volts respectively in series? Would you connect these cells La parallel? 
Give reason for your answers. 

10. Derive an equation for the current maintained in a circuit by a 
series-multiple combination of cells. 



PROBLEMS 

1. A bell circuit is operated by 3 dry cells in series. Each cell has an 
E. M. F. of 1.4 volts, and an internal resistance of 0.4 ohm. What current 
will the bell receive if its resistance, including the hne, is 20 ohms ? Ans. 
0.198 ampere. 

2. To operate, a small motor 6 Grenet cells are connected in parallel. 
Each cell has an E. M. F. of 2 volts and an internal resistance of 0.6 ohm. 
The total external resistance is 0.9 ohm. What current will the motor 
receive ? Ans. 2 amperes. 

3. Some miniature incandescent lamps are lighted by 24 Edison- 
Lalande cells, arranged 4 in series and 6 groups in parallel. Each cell 
has an E. M. F. of 0.7 volt and an internal resistance of 0.15 ohm, and 
the external circuit has a resistance of 0.21 ohm. What current do the 
lamps receive? Ans. 9 amperes. 

4. Four Leclanche cells, E. M. F. of 1.4 volts each, and internal resis- 
tance of 0.4 ohm each, are to send a maximum current through a circuit of 
15 ohms resistance. Would you connect the cells in series or in parallel ? 
Determine the maximum current. Ans. 0.337 ampere. 

5. Calculate the current from all symmetrical combinations of 6 cells 
connected to an external resistance of 2 ohms. Each cell has an E. M. F. 
of 1.4 volts and an internal resistance of 0.5 ohm. Ans. Series = 
1.68 amperes; parallel = 0.67 ampere; 2 in series, 3 groups in parallel = 
1.2 amperes; 3 in series, 2 groups in parallel = 1.52 amperes. 

6v A Grenet cell (E. M. F. 2.3 volts, internal resistance 0.2 ohm) and a 
dry cell (1.5 volts and 0.6 ohm internal resistance) are connected in parallel. 
What current will flow through the connecting wire ? Ans. 1 ampere. 

7. A Daniell cell, Grenet cell, and Leclanche cell having E. M. F.'a 
of 1.1, 2.0, and 1.4 volts and internal resistances of 2.0, 0.3, and 0.5 ohms 
respectively, are connected in series to a resistance of 3 ohms. What 
current flows through the external resistance? Ans. 0.77 ampere. 

8. Eight cells are joined in series-multiple; 4 cells in multiple, 2 groups 
in series. Fig. 94. Each cell has an E. M. F. of 2 volts and an internal 
resistance of 0.5 ohm. The cells are connected to a small incandescent 
lamp having a hot resistance of 0.75 ohm. What current will the lamp 
receive ? Ans. 4 amperes. 



LESSON X 

PRACTICAL APPLICATION OF OHM'S LAW 

Electromotive Force and Potential Difference — Hydraulic Analogy to 
Illustrate Volts Lost — Measurement of Electric Pressure — 
Potential Difference, Current and Resistance of Parallel or Divided 
Circuits — Volts Lost in an Electric Circuit — Distribution of Poten- 
tial in a Circuit — Volts Drop in Wiring Leads — Variation of Poten- 
tial Difference with Variation of External Resistance — Table IX — 
Questions and Problems. 

127. Electromotive Force and Potential Difference. — Volts 
lost or volts drop in a Circuit. — Electromotive force is the 
total force generated; potential difference is any part of the 
total E. M. F. The E. M. F. of any generator is not available 
for use in the external circuit, since part of it is required to 
cause the current to flow through the internal resistance of 
the generator (battery or dynamo). By the expressions fall 
of potential, drop or volts lost in any part of a circuit is meant 
that portion of the E. Mo F. which is used in causing the current 
to flow between the two points considered. For example, the 
*' voltage drop" across a lamp means the potential difference 
across the lamp terminals; it is the force which is causing the 
current to flow through the lamp. Two "volts lost on the 
line" means that this much pressure is lost or used in sending 
the current through the line. The E. M. F. is the sum of all 
the potential differences, as, the drop on the line plus the drop 
across the lamp plus the drop on the. internal resistance of the 
generator. The term volts lost or volts drop implies that energy 
is lost, since electric power is the product of volts and amperes, 
Formula (54); pressure could not be "lost" in any circuit 
unless a current had been transmitted by it. 

128. Hydraulic Analogy to Illustrate Volts Lost. — A hy- 
draulic analogy may assist somewhat in understanding the 
fall of potential or volts drop in an electric circuit. In Fig. 95, 
T is a cylindrical tank filled with water under pressure due to 

128 



PRACTICAL APPLICATION OF OHM'S LAW 129 

the weight of the piston P, and AB is a pipe for transmitting the 
water to point B. With the valve at B closed the pipe is full 
of water, but there is no current through it. The gauges at 
A and B each indicate 60 pounds per square inch, which rep- 
resents the water-motive-force or power to move the water. 
When the valve is opened half on and a current of water is 
passed through the pipe, the pressure on the gauge at A is 
still 60 pounds,^ while at B it is only 50 pounds. The weight 
of water is neglected. There is thus a difference in pressure 
of 10 pounds between the two points A and B, and this force 
has been used or lost in overcoming the friction or resistance 

~*3 Pressure of Piston 
% 60lbs.p?rSq.ln. 

p fl,, AK Difference in Pressure 10 lbs. >jB 



Fig. 95 , — Tank of Water and Transmission Pipe to Illustrate the Fall 

of Potential. 

offered by the inner surface of the pipe to the running water. 
The available pressure at the B end of the pipe, which might 
be used for driving a turbine, is only 50 pounds, w^hile the total 
pressure is 60 pounds. There is thus not a loss of quantity of 
water, but a loss of energy, as work has been performed in 
moving the water. Suppose the pipe to be of uniform bore 
and 10 feet long, then a gauge inserted at a point one foot 
from A would indicate 59 pounds; at two feet, 58 pounds, 
etc.; or there is a gradual fall or drop of pressure along the 
pipe which is directly proportional to the length when the 
resistance is uniform, or a drop or " loss of head " of one pound 
per foot in length. 

1 The term "pound" is used as an abbreviation of the pressure unit 
"pound per square inch." 



130 



LESSONS IN PRACTICAL ELECTRICITY 



The difference in pressure between any two points is the 
pressure required to send the current between these points, 
and is found by subtracting the pressure of that gauge which is 
more distant from the generating source, from the pressure 
of the gauge nearer to it. The valve is now fully opened and 
the gauge at A still indicates. 60 pounds, while that at B now 
indicates 40 pounds. A difference in pressure of 20 pounds 
i^ required to cause the increased current to flow through 
the pipe, leaving only 40 pounds available pressure to be 
applied to the turbine at B. A force of two pounds is required 

Pressure of Piston 
60 lbs. per Sq. In. 



A 

eoibs. 



59lbs. 



55 lbs. 53 lbs. 






SO/bs. 



-.Wafer. 



< — lib. — J<- 




-4lbs:—>!^-'2lbs. 

/Ofeet 

-Difference in Pressure 10 lbs. 



Fig. 96. — Hydraulic Analogy of the Fall of Potential. 



to send the increased current through each foot of the pipe, 
and the sum of the pressures lost in the 10 feet equals 20 pounds, 
or the difference in pressure between the points A and B. If 
the transmitting pipe considered above is replaced by one 
much larger in diameter, the resistance will be less, and less 
pressure therefore will be lost in transmitting the water, so 
that a greater available pressure will result. 

Suppose that the pipe AB is composed of several pieces of 
different sizes joined as in Fig. 96; with no current flowing 
the pressure at gauge B is equal to that at A. With the valve 
opened half on, gauge A indicates 60 pounds and gauge B 50 
pounds, as before, making a loss in pressure between the two 
points A and B of 10 pounds, which causes the current to flow 
between them. While the current of water may be the same 
as before and the total pressure lost also the same, the distri- 
bution of the lost pressure is not the same, since the resistance 
of the pipe is not uniform, it being practically a number of 



PRACTICAL APPLICATION OF OHM'S LAW 131 

pipes of different sizes, and therefore of different resistances, 
connected in series. The greatest difference in pressure will 
be between points having the greatest resistance, such as the 
length of pipe of small diameter, where four pounds are re- 
quired to send the current of water through this section of 
the pipe, while only two pounds are required to send the same 
current through the larger adjacent section. The opposition 
to be overcome in the pipe of smaller diameter is twice as great 
as in the larger pipe, since twice the pressure is required to 
send the same current through it. In hydraulics, calculations 
are made to deliver water at a certain rate of flow and under 
a certain pressure, in which case the pressure and energy lost 
in transmitting the water must be considered. The same is 
true in calculating the sizes of pipes for gas lighting, and of 
wires for carrying electric currents, H 218. 

129. Measurement of Electric Pressure. — To measure 
electric pressure (volts) between two points requires galva- 



t 



@. 



^H^ 




Fig. 97. — Connection of a Voltmeter and an Ammeter 
to a Circuit. 

nometers of very high resistance, and when properly calibrated 
their scales are graduated directly in volts and the instruments 
are then termed voltmeters, H 218. 

Voltmeters are connected directly across the line, the voltage 
of which is required, or in parallel with the conductor between 
the ends of which the P. D. is required. A voltmeter is never 
connected in series with the line, and an ammeter never across or 
in parallel with the line, but always in series with it (see Fig. 
97). Figs. 98, 101 to 107 illustrate the proper connections 
for measuring the potential differences in the various parts of 
a circuit. 

Experiments 52 and 53 that follow illustrate the use of a 
voltmeter for measuring the voltage across the parts of a 
circuit; the experiments also prove that the voltage across any 
part of a series circuit is proportional to the resistance of that 



132 



LESSONS IN PRACTICAL ELECTRICITY 



part. The current value in any part of a series circuit is always 
the same. 



Experiment 52. — Four spools of wire, A, B, C, and D, Fig. 98, with 
resistances of 2, 3, 4, and 6 ohms respectively, are connected in series 
and to a battery. The spools may represent lamps, magnets, or any other 
electrical devices. When the battery circuit is closed through the above 
circuit, and the voltmeter .connected directly across its terminals, 30 volts 

potential difference is indicated. 



A- 2 Ohms 

rmmm 

H 4yo//s K 



B- 3 Ohms 




6 Ohms 



50 Volts 



Fig. 98. — Measuring the Voltage 
Drop in an Electric Circuit. 



The total external resistance is 2 + 3 
+ 4 + 6 = 15 ohms, and the 30 volts 
potential difference indicated by the 
voltmeter is the pressure causing the 
current to flow through this external 
resistance. The current is, by For- 
mula (27), 30 ^ 15 = 2 amperes. 
,^ ,^,,^ To measure the proportion of the 

V-j I I ^AAAAMA/ total P. D., 30 volts, causing the cur- 

rent to pass through the 2-ohm spool, 
A, Fig. 98, the voltmeter is placed in 
parallel with it, or connected to the 
points H and K, and indicates 4 volts. 
When the voltmeter is connected 
across the 3-ohm spool B, 6 volts are indicated. The current is the same 
as through spool A, the resistance, however, being 1| times as great as A 
requires also 1| times the voltage that A requires. Spool C has 4 ohms, 
or twice the resistance of A, and the voltmeter indicates 8 volts. 

By Formula (28) the voltage required to send 2 amperes through 4 
ohms is calculated tobeE=IxR=2x4=8 volts; also in spool A the 
calculated voltage is 4 volts. The 
results of the measurements across the 
four spools by a voltmeter are indi- 
cated in Fig. 98, the sum of the volts 
drop on all the spools is 4+6+8 
+ 12 =30 volts, or the potential 
difference measured at the battery. 
The total external resistance is 15 
ohms, the current 2 amperes, and by 
Formula (28) the potential difference 
equals IxR=2xl5=30 volts. 
Suppose the internal resistance of the 
cells, r, is 5 ohms, then E = I x r or 
2 X 5 =10 volts drop in the cells. 

If the voltmeter is connected across the battery it indicates the P. D. of 30 
volts, when 2 amperes are flowing. If the external circuit is now opened the 
voltmeter indicates the E. M. F. of the cells, which is the sum of all the 
former potential differences in the circuit or 30 + 10 = 40 volts E. M. F, 




Fig. 99. 



Fall of Potential along 
a Wire. 



PRACTICAL APPLICATION OF OHM'S LAW 133 

Experiment 53. — In Fig. 99, a fine German silver wire, AB, uniform 
in size, is stretched on a board between binding posts and a scale of inches 
arranged directly beside it. The wire is connected in circuit with one or 
more cells, preferably of the DanieU type, so that the current flowing 
through the wire will be constant. If the terminals of a galvanometer 
or voltmeter are held on the wire, so as to include a portion of its length 
between them, as in Fig. 99, the potential difference between the points 
embraced will be represented by the value of the deflection. One ter- 
minal may be fixed at point A and the other terminal gradually moved 
along the wire toward B. The deflection increases in approaching B. 
For example, with six inches of wire between voltmeter terminals the 
drop is 0.4 volt; 12 inches, 0.8 volt, etc. 

Since the current is the same in all parts of the circuit, the 
same deflection will be produced for equal distances on the 
wire, provided its resistance is uniform. If a copper wire of 
the same size is connected in series with the German silver, 
the volts drop on 12 inches of copper will about equal the 
drop on 1 inch of German silver, since the latter has about 
twelve times the resistance of copper, and to send the same 
current through it, therefore, requires twelve times the pres- 
sure. The student should make a table of comparative lengths 
and deflections for several different wires of the same diameter 
joined in series, as the following: 



Inches 


Copper 


German silver 


Iron 


Deflection 


Deflection 


Deflection 


5 

10 

15 

Etc. 









130. Potential Difference, Current and Resistance of Parallel 
or Divided Circuits. — The potential across each branch of a 
parallel circuit is the same as the voltage between the points 
where the branches divide and where they again unite. In 
Fig. 100 the voltage across resistance A is the same as the 
voltage across the combination A and B since they are both 
connected between the same points, X and Y. The total cur- 
rent in a parallel combination" equals the sum of the currents 



134 



LESSONS IN PRACTICAL ELECTRICITY 



in the several branches; in Fig. 100 the current flowing from 
X to Y equals the current in A plus the current in B. 

To FIND THE POTENTIAL DIF- 
FERENCE TO BE MAINTAINED 
BETWEEN THE POINTS WHERE 
SEVERAL CIRCUITS BRANCH AND 
WHERE THEY AGAIN UNITE: 

Multiply the sum of the 
currents in all the branches 
by the joint resistance of the 
Fig. 100. — Finding the Currents branches. 
through the Branches of a Divided Let Ii, I2, etc. = currents in 

the branches, 
E = potential difference across branches, 
J. R. = joint resistance of the branches. 
Then 



A -8 Ohms 
B-l? Ohms 

-mm—' 



o 



E = (Ii + I2 + etc.) X J. R. 



(46). 



Problem 63. — Two coils A and B, having resistances of 8 and 12 
ohms respectively, are connected in parallel (Fig. 100). Find the poten- 
tial difference required to send 15 amperes through A and 10 amperes 
through B. 

1 1 3+2 5 

By \ 109 joint conductance =--\-—_^ = —77- = — mho. 



12 



24 



24 



24 
Joint resistance = — =4.8 ohms. 

o 



= 120 volts. 
A PARALLEL 



By Formula (46) E = (Ii + I2) x J. R. = (15 + 10) x 4 

To FIND THE CURRENT IN ANY BRANCH OF 
CIRCUIT : 

Divide the potential difference between the points ivhere the 
branches divide and unite by the resistance of that branch. 

Problem 64. — Find the current through each branch of the divided 
circuit in Fig. 100, if the potential difference is 24 volts. 

E 24 

R ~ 8 



By the above statement the current in A is I 



3 amperes, and 



24 
the current in B is — = 2 amperes. 



The joint resistance of a parallel combination can generally 
be found by a direct application of Ohm's Law as well as by 



PRACTICAL APPLICATION OF OHM'S LAW 



135 



50 Volts 



the method of H 109, although .the conductance method is 
sometimes more convenient. 

The separate resistance of any branch of a multiple circuit 
may be found by dividing the potential difference across the 
branch by the current flowing through that branch, according 
to Ohm's Law. 

131. Volts Lost in an Electric Circuit. — Consider now an 
electric circuit in which a generator (battery or dynamo) is 
supposed to maintain a constant pressure of 60 volts between 
two parallel lines at the point A, Fig. 101, as indicated by a 
high-resistance galvanometer or voltmeter. With no current 
flowing from the generator the voltmeter will indicate 60 volts 
at point B (neglecting the pressure used to transmit the small 
current used by ^-^^ 

the voltmeter). (p^^ 'J'"' (^ ' 
By closing the 
switch at the 
right, the lamp 
L is lighted, and 
an ammeter in- 
dicates 1 ampere 

flowing through ^^^ _ ^^^^^ .^ ^^ ^j^^^^.^ ^.^^^^_ 

the Circuit, ihe 

voltmeter at A still indicates 60 volts, but the voltmeter at B 
only 50 volts. There is, therefore, a difference in pressure 
between points A and B of 10 volts, which is used in overcoming 
the resistance of the line and causing the one ampere to flow 
through it. The available pressure at point B to perform useful 
work in the lamp is, therefore, only 50 volts and causes one 
ampere to flow through it. There is no loss of current but a loss 
of energy on the line, that is, work has been performed in trans- 
mitting the current from A to B, just as in the case of the water 
in the pipe line of 1[ 128.^ If 10 volts are required to send one 
ampere through the line its resistance, by Formula (29), wifl be 
10 ohms. 

If the wire is of uniform area and 10 feet in length from 
A to B, the voltmeter will indicate 59 volts when placed across 
the hne at points 1-1, one foot distant from A; 58 volts at 2 
■ 1 See also Lesson XI, 




/O Feet ■ 



136 



LESSONS IN PRACTICAL ELECTRICITY 



feet, or points 2-2, etc. ; or the fall of potential along the line is 
directly proportional to its length and resistance. Since the 
total resistance of the line is 10 ohms, the resistance of one 
wire is 5 ohms and the difference in potential required to send 
one ampere through 5 ohms isE = IxR = lx5 = 5 volts. 
A voltmeter placed across one side of the line to include 10 
feet of its length will indicate a potential difference of 5 volts 
drop on this side, and the same drop will occur on the other side 
of the line. Since there are 5 volts drop on 10 feet of wire of 
uniform resistance the drop per foot will be J volt, or 1 volt 
for every 2 feet, etc. The voltmeter, when placed in parallel 
with any length of the wire, will indicate the difference of 
potential between the points included. 

Now turn on the switch of a second lamp of the same resis- 

tance, the am- 
<;^^ 6 Volts <(^^ 10 Volts <Z^ 40 Volts meter will now 

T~LX ^NJ~t indicate 2 am- 

peres (Fig. 102). 
The voltmeter at 
A still indicates 
60 volts as be- 
fore, but that at 
B now indicates 
only 40 volts. The difference in pressure between points A 
and B is 20 volts, since twice the current through the same 
resistance requires double the pressure to be applied. The 
available pressure applied to the lamps is 40 volts. If the 
wires considered above were just double the area, only one 
half of the pressure would be lost on the leads, and therefore 
one half of the energy would be lost, and a higher P. D. at 
point B would be maintained. 

Suppose the transmitting line to be composed of several 
wires of different sizes connected in series as represented by the 
heavy and thin lines in Fig. 103. With one lamp connected 
at B, the voltmeter may read 50 volts, as before, but the fall 
of potential or drop on the line of 10 volts will not now be uni- 
form, since the resistance is not uniform. The greatest poten- 
tial difference or drop will be between the pomts of highest 
resistance. Consider the equal lengths of wire E F and F G 




Fig. 102. — Volts Drop in an Electric Circuit. 



PRACTICAL APPLICATION OF OHM'S LAW 137 




50 Volts 



of unequal areas. The current is the same through each, but 

the voltmeter indicates 3 volts when connected across points 

E F, and only 1 volt when placed across points F G. The 

thin wire E F 

has three times 

the resistance of 

the wire F G, 

since three times 

the pressure is 

required to send 

the same current 

through it. The drop in volts in other portions of the line may 

be measured in the same manner, the sum of all the readings 

being equal to the total loss on the line, or 10 volts. 

132. Distribution of Potential in a Circuit. — In the fore- 
going illustrations the pressure was assumed to be maintained 
constant at point A. Consider now a battery or generator D, 
Fig. 104, with an internal resistance (r) of 4 ohms, connected 
to one lamp at B, 10 feet distant from A. The voltmeter at 



CD B 

Fig. 103. — Drop in a Non-uniform Electric Circuit. 



SVo/ts 



4Volts^ \ ^-^ ^^ 
r-AOhrrk Z^ 1 \A .M.7 / 




Leads 10 Ohms 
Ampere 



Fig. 104. 



E. M. F. and Potential Difference in an Electric 
Circuit. 



A indicates 60 volts as before, and with one ampere flowing 
through the lamp, 50 volts at B. Ten volts are required to 
send one ampere through the lead wires, and since the internal 
resistance of the generator is 4 ohms, 4 volts will be required 
to send one ampere through it. Formula (28). The total 
pressure or E. M. F. is, therefore, 4 + 10 + 50 or 64 volts. 
The voltmeter across the generator terminals, however, indi- 
cates the potential difference or that portion of the E. M. F. 
available in the external circuit, 60 volts. If the lamp at B 
is turned off the voltmeters at both points A and B will indicate 
64 volts, or the E. M. F. of the source of electricity. Now 



138 LESSONS IN PRACTICAL ELECTRICITY 

connect two lamps in circuit, Fig. 105; the resistance of one 
lamp is 50 ohms, and of two in parallel is 25 ohms, Formula 
(30) . The total resistance of the circuit is R + r = 10 + 25 + 
4 = 39 ohms, and the current, therefore, equals 64 -^ 39 or 
1.64 amperes. Formula (27). The voltmeter at B indicates 
1.64 X 25 = 41 volts, Formula (28), while the voltmeter at A 
indicates 1.64 x (10 + 25) = 57.4 volts potential difference at 
the generator terminals. The- drop on the internal resistance 
is 4 X 1.64 = 6.56 volts. Total E. M. F. is 6.56 + 57.4 = 64 
volts (nearly). If the lamps require 50 volts to send sufficient 
current through them to give the proper amount of light, with 
40 volts across their terminals they will now burn dimly, 

\m) 57.4 Volts (\m) 41 Yolfs 

Leads 10 Ohms 



A 



^^ 



1.64 Amperes 



J.R=25 
Ohms 






Fig. 105. — E. M. F. and Potential Difference in an 
Electric Circuit. 

since each lamp does not receive one ampere, as before. The 
total E. M. F. must be increased, say by adding more cells 
in series, or increasing the field strength of the generator, if 50 
volts are to be maintained across the two lamps in parallel. 
If one lamp is then turned out the other lamp receives a greater 
pressure than 50 volts, since the drop on the leads and internal 
resistance is less when the current through them is diminished. 
The E. M. F. must therefore be decreased as the current is 
decreased and increased when the current increases. In a 
battery installation for lighting lamps a special switch is used 
to connect or disconnect several end cells, as the voltage regu- 
lation may require. This switch is called an end-cell switch. 

In IfTI 131 and 132, the resistance of the leads has been con- 
siderably exaggerated, and consequently also the volts drop, in 
order to emphasize the effects. In practice the drop on com- 
mercial lighting and power circuits is much less (see If 335), so 
that the voltage will not change widely with variations of load. 

Problem 65. — Eight arc lamps are connected in series to a series 
generator, Fig. 106; each lamp requires 45 volts and 10 amperes. The 
resistance of the series field is 4.5 ohms and the armature has a resis- 



PRACTICAL APPLICATION OF OHM'S LAW 1B9 



tance of 4.5 ohms, (a) What pressure will be indicated by a voltmeter 
placed across the brushes? (b) What is the E. M. F. of the generator? 

45 



By Formula (29) 



..! = 



10 



= 4.5 ohms per lamp. 



Resistance of 8 lamps in 
series = 8 X 4.5 = 36 ohms. 

By Formula (28) E = I 
X R = 10 X 36 = 360 volts 
potential difference (a). 

Total resistance r + R = 
4.5 + 4.5 + 36 = 45 ohms. 

By Formula (37) E = I 
X (R + r) = 10 X 45 = 450 
volts (b). 



'-45 Volts 
■4.5 Ohms-'' 




45 V. 



45V. 



-E. M. F. and Potential Difference 
in a Series Arc-light Circuit. 



(^^ [^ ^^^ 



133. Volts Drop in Wiring Leads. — The size of wire re- 
quired to conduct a given current a certain distance may be 
readily obtained by finding its resistance by Ohm's Law. 
In Fig. 107 a generator, D, is supplying current, 20 amperes, 
to a number of lamps, L, located at a distance of 100 feet. 
The voltage at the generator is 112 volts and at the lamps is 

110 volts. There 
A ^.--' 1 Volt Lost ^^^^ ^ ^^g 2 volts drop on 

the line, or two 
volts are required 
to send 20 amperes 
through the 200 
feet of copper wire. 
By Formula (29) 
the resistance of the line equals E-^I = 2-^20 = 0.1 ohm per 
200 feet, or 0.5 ohm per 1000 feet. From the wire table, on 
page 67, is found the nearest size of wire corresponding to 
0.5 ohm per 1000 feet, which is a No. 7 B. & S. gage. 

As a check upon this calculation the table of carrying ca- 
pacities, H 236, should be consulted to further ascertain whether 
the wire is large enough to carry the current without undue 
temperature rise. Refer also to ^ 335. 

134. Variation of Potential Difference with Variation of 
External Resistance. — 

Experiment 54. — Connect a voltmeter to a Grenet cell and also a 
variable resistance, R, in series with an ammeter, Fig. 108. With switch 



■-^J12 Volts 



Fig. 107. 



no Volts ^^^ 

— / Volt Lost -'' 

Volts Lost in Wiring Leads. 



140 



LESSONS IN PRACTICAL ELECTRICITY 



S open, the voltmeter indicates 2 volts or the E. M. V. of the cell. Adjust 
arm A of the rheostat so that a high resistance will be connected to the 
cell, say 100 ohms, when switch S is closed. The voltmeter now indi- 
cates 1.999 volts, or the potential difference is nearly equal to the E. 
M. F. when the external resistance is high, since very little current flows. 
Now reduce R to about 9.8 ohms; if the cell's 
resistance = 0.4 ohm, r + R = 10 ohms and the 
current = 0.2 ampere. The voltmeter indicates 
I X R = 0.2 X 9.6 = 1.92 volts potential difference 
which is causing 0.2 ampere to flow through 9.6 
ohms; the remaining 0.08 volt is required to send 
the same current through the internal resistance. 
Reduce the external R to 0.4 ohm and the volt- 
meter indicates 1 volt P. D. Since the external 
resistance is now equal to the internal resistance 
there is 1 volt drop inside the cell. Short-circuit 
the cell by a very low resistance and the voltmeter 
indicates practically zero, the current from the cell 
is a maximum and all of the E. M. F., 2 volts, is used in sending the current 
through the cell's internal resistance. The preceding experiments may 
be summed up in the following table, which can be verified by the appara- 
tus in Fig. 108: 

Table IX. Variation of Current, Pressure and Resistance 




Fig. 108. — Varia- 
tion of P. D. and Cur- 
rent with a Variation 
of Resistance. 



Ohms External Circuit, R 


Volts across Battery, P. D. 


Amperes, I 


Infinity 


Equal to E. M. F. 





Great compared with r 


Very httle less than 
E. M. F. 


SmaU 


Any value 


-^— X E. M. F. 

R +r 


E. M. F. 

R+r 


Small compared with r 


Small 


Large 








Maximum and equal to 

E. M. F. 

r 



The following formulae derived from Ohm's Law will be 
found useful in calculating the internal resistance and potential 
difference: 

Let E = E. M. F. in volts, 
P. D. = potential difference in volts, 

II = resistance of external circuit in ohms, 
r = internal resistance in ohms. 



PRACTICAL APPLICATION OF OHM'S LAW 141 

Then the current by Formula (35) is 

E 



Also I = 



R + r 
P. D. 



R 

By combining the first and second equations we get, 
P. D. ^ E 
R ~ R + r' 

or , P.D. =^L^. . (47). 

R + r 

Eliminating R from the first and second equations, there 
results 

E - Ir _ P. D. 

~T~" I ' 
from which 

I = ^-fP-, . .• (48). 

E - P. D. 
or r = • (49). 

By Formula (49) a cell's internal resistance may be measured 
by noting the voltmeter and ammeter readings when it is 
connected, as in Fig. 108. 

Problem 66. — The E. M. F. of a Leclanche cell is 1.4 volts, and its 
P. D. measured at the battery terminals when 0.8 ampere is flowing is 
1 volt. What is the cell's internal resistance ? 

, ,_, E -P. D. 1.4-1 1 , 

By Formula (49) r = = = — — — - = - ohm. 

i U.o z 

Problem 67. — The E. M. F. of a generator is 112 volts; the resistance 
of its circuit is 5 ohms; the resistance of the generator armature is 0.05 
ohm. What P.'D. will a voltmeter indicate when placed across the brushes ? 

By Formula (47) P. D. = ^^ ^ 5 ^0^05 ^ ^^^'^ ^^^*^- 

QUESTIONS 

1. Distinguish between E. M. F. and potential difference. 

2. What do you understand by the term "drop" or "volts lost" ? 

3. Make a sketch of an electric circuit, showing how you would place 



142 LESSONS IN PRACTICAL ELECTRICITY 

an ammeter in the circuit to read the current; also a voltmeter to read 
the potential difference of the circuit. 

4. The E. M. F. of a cell measured by a voltmeter is 1.8 volts. When 
connected to a spool of wire the voltmeter across the battery terminals 
indicates only 0.7 volt. Account for the volts lost, and state what pressure 
is applied to the spool. 

5. Four coils of wire having resistances of 1000, 100, 10, and 1 ohms 
respectively are successively connected to a battery of 10 volts E. M. F. 
What will be the comparative value of the readings of a voltmeter placed 
across the terminals as compared with the E. M. F.? State also the 
comparative current strength in each case. 



PROBLEMS 

L Find the size of wire required to conduct current to 100 220-ohm 
lamps in parallel, located at a distance of 125 feet from the generator, 
which maintains a constant pressure of 112 volts at its terminals. The 
lamps should receive 110 volts. Ans. No. 2 B. & S. 

2. What P. D, must be maintained at the terminals of a generator 
so that 150 lamps, in parallel, each requiring 0.5 ampere at 110 volts, 
will receive their proper current ? Resistance of leads 0.02 ohm. Ans. 
111.5 volts. 

3. If the internal resistance of the generator armature in Problem 2 is 
0.05 ohm, what E. M. F. is developed by the machine ? Ans. 115.25 volts. 

4. How much resistance must be inserted in series with two 50-volt 
50-ohm lamps, to allow them to be placed in series across a 220- volt circuit ? 
Ans. 120 ohms. 

5. We desire to run a motor, requiring 1 ampere, at 6 volts from a 
supply circuit of 110 volts potential difference. If two 50-volt 50-ohm 
(hot) incandescent lamps are connected in series with the motor, how 
much additional resistance must be added to meet the requirements? 
Ans. 4 ohms. 

6. Three coils. A, B, and C, having resistances of 6, 8, and 12 ohms 
respectively, are connected in parallel and then in series with a coil D of 
2 ohms; if 9 amperes flow& through coil B of 8 ohms, how much current 
flows through each of the other coils ? Ans. 12 amperes in A, 6 amperes 
in C, 27 amperes in D. 

7. What is the P. D. maintained across the parallel circuit in Problem 
6, and what is the total pressure across the entire circuit ? Ans. 72 volts; 
126 volts. 

8. The two field magnets of a bipolar generator have a resistance of 
55 ohms each, and are connected in series and then connected across the 
brushes where 110 volts are maintained, (a) What is the field exciting 
current ? (6) What will be the exciting current when the fields are con- 
nected in parallel and across the brushes ? Ans. (a) 1 ampere;. (6) 4 amperes. 

9. You are required to construct an electric heater for a trolley car of 
No. 16 B. & S. iron wire which shall operate on 10 amperes. Assuming 



PRACTICAL APPLICATION OF OHM'S LAW 143 

that the potential difference between trolley wire and tra,ck is 500 volts, 
find the length of wire required so as to place the stove in parallel with 
the circuit. (Neglect the rise in resistance due to the heat.) Ans. 2038 
feet.i 

10. (a) How much resistance would you insert in circuit with a 50-volt 
50-ohm incandescent lamp to place it across a 110-volt circuit? (b) How 
many feet of No. IS B. & S. German silver wire are required to make a 
rheostat for this purpose ? Ans. (a) 60 ohms; (6) 759 feet.^ 

11. Four electromagnets having resistances of 4, 6, 8, and 10 ohms 
respectively, are connected in series and to a battery having an internal 
resistance of 2 ohms. When the switch is closed a voltmeter, across the 
battery terminals, indicates 56 volts, (a) What will be the indications 
of a voltmeter when paralleled with each spool? (6) What will the 
voltmeter indicate when placed across the cells when the magnets are 
disconnected? Ans. (a) 8, 12, 16, and 20 volts; (6) 60 volts. 

12. What will be the drop on 500 feet of No. wire used as an overhead 
trolley line at the instant when it is supplying current to four cars, each 
requiring 70 amperes ? Ans. 14.2 volts. ^ 

1 The student is advised to calculate resistances rather than take them 
from the wire table. 



LESSON XI 

ELECTRICAL WORK AND POWER 

Force — Different Kinds of Force — Mass and Weight — Work — Power 

— Horse Power of a Steam Engine -■ — Difference between Energy, 
Force, Work, and Power — Electrical Work — Electrical Power — 
Heat and Work — Equivalents of Mechanical and Electrical Work 

— Electrical Horse Power — The Kilowatt — The Watt-hour and 
Kilowatt-hour — Electrical Power Calculations — Power from Cells 

— Efficiency — Questions and Problems. 

135. Force. — Force is defined as that which produces mo- 
tion, or a change of motion, in matter; thus force must always 
be apphed to any body to cause it to move. To increase, 
decrease, or stop this motion, that is to change it, force must 
again be apphed. For example, to start a loaded wheel- 
barrow force must be applied, either by pushing or pulling it, 
but when it is set in motion less force will be required to keep 
it in motion; to cause a change in motion, that is to increase 
or decrease the speed, extra force must be applied. Force 
does not always produce motion, in some cases it only tends 
to produce motion; thus, when a man tries to push a laden 
freight car he applies all his muscular force, but no motion 
results. 

136. Different Kinds of Force. — There is the force of 
gravitation, in virtue of which all bodies free to move will fall 
from a higher to a lower level. The force exerted by a man 
riding a bicycle or by a horse drawing a carriage are examples of 
muscular force. An engine draws a train of cars by reason of 
the mechanical force applied, which is due to the expansion 
of the steam in the engine cylinder. A mixture of air and illu- 
minating gas in a room is ignited and the explosion wrecks 
the room; the action is due to the chemical force exerted. 
The force which produces or tends to produce a flow of elec- 
tricity is electromotive force. The force which sets up mag- 
netic lines of force is magnetomotive force. The rate at which 

144 



ELECTRICAL WORK AND POWER 145 

a train moves depends upon the force exerted by the engine, 
so also, the rate of flow of electricity depends upon the amount 
of electromotive force applied. 

137. Mass and Weight. — The mass of a body is the 
quantity of matter in it; the weight of a body is due to the 
force of gravity acting upon this matter. Since the force of 
gravity diminishes as we ascend from the earth's surface, the 
attraction for a mass of matter will diminish, or it will weigh 
less on the top of a high mountain than at the sea level; the 
mass of matter, however, would be the same in each case. 
Weight is not, therefore, the same thing as mass, but we can 
conveniently measure a body by its weight. 

138. Work. — Work is done when force overcomes a re- 
sistance and moves the body on which it acts, or, work is force 
acting through space. The amount of work done is measured 
by the product of the force and the distance through which 
the body moves, or 

work = force X distance, 
or work = pounds x feet = foot-pounds. 

Work is not always done when a force acts; for instance, 
a man pushes with all his force against a brick wall; he is 
exerting force, but doing no work because no motion results, 
nor is any resistance overcome. If a weight be lifted, work 
is done directly in proportion to the weight and to the dis- 
tance through which it was moved. Thus, the work done in 
lifting 4 pounds to a height of 3 feet is equivalent to 12 foot- 
pounds of work. Exactly the same work is performed when 
2 pounds are raised 6 feet; or 6 pounds raised 2 feet; or 12 
pounds raised one foot. Work does not always consist in 
raising weights; the steam engine does work by hauling a 
train, due to the expansive force of steam acting upon the 
piston; an explosion of powder in a cannon causes an iron 
ball to traverse a certain distance. The chemical action in a 
storage battery sets up a force which causes a current to flow 
through an electric motor, and the motor drives an auto- 
mobile weighing so many pounds a certain nimiber of miles. 
The work in each case is measured in foot-pounds. Whether 
work be done mechanically, chemically, thermally, or electri- 



146 LESSONS IN PRACTICAL ELECTRICITY 

cally, it can be expressed in foot-pounds. The total amount 
of work done is independent of time, that is, the same work 
may be performed in one hour or one year. When different 
amounts of work performed in different amounts of time are 
to be compared, then reference is made to the time rate of 
working, or the power. 

139. Power. — Power is the rate at which work is done and is 
to be distinguished from the total amount of work to be done. 

work 



Power 



time 



foot-pounds p ^ 1 'J r J- 

or - — -^ = toot-pounds per unit of time. 

time 

For example, it requires four hours for a particular engine 
to draw a train from one station to another, while another 
engine may draw the same train the same distance in two 
hours. One engine is thus twice as powerful as the other, be- 
cause it can do the same work in one half the time. When 
the train had reached its destination it would have repre- 
sented the same amount of work done, no matter whether it 
had traveled at one mile per minute or one mile per hour, 
leaving, of course, friction and air resistance out of account. 

Power is estimated according to the amount of work done in 
a given period of time. As mechanical work is measured in 
foot-pounds, mechanical power would thus be so many foot- 
pounds per minute, or per second. Another mechanical unit 
of power is the horse power. 

One mechanical horse power = 33,000 ft. lbs. per 
MINUTE, or 

= 550 ft. lbs. per second. 

60 ^ 

If a body weighing 33,000 pounds be raised one foot every 
minute then we have a rate of working equal to one horse 
power; or if 16,500 pounds be raised two feet per minute, 
the rate of working is the same, one horse power. When we say 
that an engine is developing 40 horse power we mean that it 
is performing 550 x 40 = 22,000 foot-pounds of work every 
second. 



ELECTRICAL WORK AND POWER 147 

140. Horse Power of a Steam Engine. — The horse power 
of a steam engine may be readily calculated from data ob- 
tained from it while it is working. The mean pressure of the 
steam upon the piston is found by attaching a recording in- 
dicator to the steam cylinder which shows graphically the vari- 
ous steam pressures during a stroke of the piston. From this 
"card," as it is termed, the average or mean effective pressure 
throughout the stroke is obtained. The speed of the engine 
must be noted while the card is taken, but the length of stroke 
in feet and the area of the piston-head in square inches should 
be previously obtained. 

The following formula may then be used to ascertain the 

rate of working, or horse power developed, corresponding to 

the above conditions: 

', , , . PxLxAxN ,__. 
horse power oi steam engme = , (50). 

ooUUU 

where P = mean effective steam pressure in pounds per sq. in. 
(from indicator card), 
L = length of stroke in feet, 
A = area of piston-head in square inches, 
N = number of strokes per minute (twice the number 
of revolutions). 

Problem 68. — The mean steam pressure of a steam engine is 45 lbs. 

per sq. iti., the speed of the engine is 275 revolutions per minute, length 

of stroke is 12 inches, area of piston-head is one-half a square foot. What 

horse power is developed by the engine? 

L = 12 inches = 1 foot, A = | sq, ft. = 72 sq. in., N = 275 rev. per min. 

X 2 strokes per rev. = 550 strokes per min. 

T> T^ 1 /rm TT TO P X L X A X N 45 X 1 X 72 X 550 ,, ^, ^ 
ByFormula(50) H.P. = ^^^ = ^^^ =54H.R 

141. Difference between Energy, Force, Work, and Power. 

— It is important that the student should thoroughly under- 
stand the meaning of the above terms. Energy is the capacity 
to do work. Force is one of the factors of work and has to 
be exerted through a distance to do work, the work being 
reckoned as the product of the force and the distance through 
which it has been applied. TVork is done when energy is ex- 
pended or when force overcomes a resistance. Povjer is the 
rate of working. 



148 LESSONS IN PRACTICAL ELECTRICITY 

142. Electrical Work. — Work is force acting through space, 
or energy expended; therefore, resistance is overcome when 
work is performed. Force may exist without work being 
performed, as when you push against a table and do not 
move it, no work is done, yet the force exists. An electrical 
force exists between the two terminals of a battery, tending 
to send a current of electricity from one to the other through 
the air. The force is not sufficient to overcome the resistance 
of the air, therefore no current flows and the battery is not 
doing any work; the same is true with a generator when 
running on open circuit. When a wire is connected across 
the battery terminals, the force overcomes the resistance 
of the wire and electricity is moved along, around or through 
the wire. The electrical work, or energy expended, is repre- 
sented by the amount of heat generated in this instance, U 237. 
With a small lamp connected to the battery, the work is repre- 
sented by the heat and light given by the lamp as well as the 
heat given off by the remainder of the circuit. The total work 
performed is the product of the force, the current, and the 
time that the current is maintained, or 

electrical work = volts x amperes x seconds. 

The unit of electrical work is the amount of work performed hy 
a current of one ampere flowing for one second under a pressure 
of one volt and is called a joule. 

Since an ampere flowing for one second is equal - to one 
coulomb, ^ 93, a joule is, therefore, one volt-coulomb and is 
analogous to the mechanical unit of work, the foot-pound. 
The joule is not as large as the foot-pound; it develops that 
1 joule = 0.7375 foot-pound, 
1 foot-pound = 1.356 joules. 

Larger units of electrical work are given in K 148. 

To FIND THE TOTAL ELECTRICAL W^ORK, IN JOULES, PER- 
FORMED IN ANY circuit: 

Multiply the volts causing the current to flow hy the current in 
amperes and the time in seconds. 

Joules = volts X amperes X seconds, 
or J = E X I X t. . » . o . . . . , (51). 



ELECTRICAL WORK AND POWER 149 

Problem 69. — A current of 20 amperes is maintained through a number 
of incandescent lamps for one hour by a pressure of 110 volts. How 
much electrical work has been performed? 

Here the time is 60 x 60 = 3600 seconds. 

By Formula (51) J = E x I X t = 110 x 20 x 3600 = 7,920,000 joules. 

To FIND THE TOTAL ELECTRICAL WORK, IN JOULES, PER- 
FORMED IN ANY PART OF THE CIRCUIT WHEN THE CURRENT 
AND RESISTANCE ARE KNOWN I 

Multiply the square of the current by the resistance, and this 
product by the time the current flows, 

J = I X R X I X t, 
or J = P X R X t (52), 

By substituting for E in Formula (51) its value I x R, we 
get Formula (52). Also by substituting the value of I, 
which equals E ^ R, in Formula (51), we obtain an expression 
to find the work in joules when the voltage and resistance are 
known, as follows: 

By Formula (51) J = ExIxt=Exfxt, 

R 

or J = — X t (53). 

K 

Problem 70. — A current of 5 amperes is passed for one-half hour 
through an arc lamp, the resistance of which is 4 ohms. How much energy 
has been expended? 

By Formula (52) J=PxRxt=5x5x4x 1800 = 180,000 joules. 

Problem 71. — The resistance of the copper cables connecting a generator 
with its switchboard is 0.1 ohm, and 2 volts are required to send the full- 
load current through them. How much energy is expended in 10 hours? 

By Formula (53) J = ^ x t = ^^f^ x 36,000 = 1,440,000 joules. 
R 0.1 

143. Electrical Power. — Power is the rate at which energy 
is expended, and is independent of the total work to be accom- 
plished. The rate of working, or the power, is found by 
dividing the total work by the time required to perform it. 

_,,,., electrical work 

Electrical power = : 

time 



150 LESSONS 'IN PRACTICAL ELECTRICITY 

The unit of electrical power is a unit of work performed in a unit 
of time; one unit is the joule per second, and is called a watt. 
Therefore, 

ioules volts X amperes X seconds 

watts =— r- = . = volts X amperes. 

seconds seconds 

One watt, therefore, equals one volt multiplied by one ampere. 

1. To FIND THE RATE IN W^ATTS AT WHICH ENERGY IS EX- 
PENDED IN A circuit: 

Multiply the current in amperes hy the pressure causing it to flow. 
Let P = watts expended, 

I = current in amperes, 
E = pressure in volts. 
Then since watts = volts x amperes, 

P - E X I (54). 

2. To FIND THE CURRENT WHEN THE POWER AND PRESSURE 

ARE known: 

Divide the watts expended by the voltage causing the current 
to flow. 

watts 



From Formula (54), amperes 



volts 



or 1=1 (55). 

3. To FIND THE PRESSURI^ WHEN THE POWER AND CURRENT 

ARE known: 

Divide the watts expended by the current flowing. 

From Formula (54), volts = , 

amperes 

or E =j (56)o 

Problem 72. — How many watts are consumed by one hundred incan- 
descent lamps connected in multiple to a 110-volt circuit, supposing each 
lamp to have a resistance (hot) of 220 ohms? 

^ E 110 1 , 

I = __ = = _ ampere per lamp. 

R 220 2 

P=ExI = 110xi=55 watts per lamp. 55 x 100 = 5500 watts. 



ELECTRICAL WORK AND POWER 151 

Problem 73. — What current is taken by a 20-watt lamp on a 100-volt 

circuit? 

P 20 
By Formula (55) I = — = — — =0.2 ampere. 
hi 100 

Problem 74. — A 500-watt motor requires a current of 10 amperes. 
What E. M. F. is necessary to operate it? 

P 500 
By Formula (56) E = - = — - = 50 volts. 
•^ I 10 

144. Heat and Work. — One of the most important dis- 
coveries in science is that of the equivalence of heat and work, 
that is, that a definite quantity of mechanical work can always 
produce a definite quantity of heat, and, conversely, this heat, 
if the conversion be complete, can perform the original quantity 
of work. 

All kinds of energy (chemical, mechanical, electrical, etc.) 
are so related to each other that energy of any kind can be 
changed into energy of any other kind. This statement is 
known as the doctrine of correlation of energy. When one 
form of energy disappears an exact equivalent of another 
form takes its place, so that the sum total of the energy is 
not changed. This is known as the doctrine of conservation 
of energy. These two principles constitute the corner-stone of 
physical science. 

145. Equivalents of Mechanical and Electrical Work. — 
Dr. Joule, of England, was the first to ascertain the rela- 
tion existing between mechanical work, heat, and electricity. 
In an experiment he caused a paddle-wheel to revolve in a 
vessel filled with water, by means of a falling weight attached 
to a cord and wound around the axle of the wheel (Fig. 109). 
The resistance offered by the water to the motion of the paddles 
was the means by which the mechanical motion of the weight 
was converted into heat, which resistance raised the tempera- 
ture of the water. From this experiment it was found that 
778 foot-pounds of work would raise the temperature of 1 
pound of water 1° Fahrenheit; also by the doctrine .(^ 144), 
the heat which would raise 1 pound of water 1° Fahrenheit 
would also raise 778 pounds 1 foot. The quantity, 778 foot- 
pounds, is called the mechanical equivalent of heat, or Joule's 



152 



LESSONS IN PRACTICAL ELECTRICITY 



equivalent. If now we heat the pound of water by a current 
of electricity until its temperature is raised 1°, we will have 
done the same work electrically as was previously done mechani- 
cally. An apparatus similar 
to the calorimeter (If 238) 
would be suitable for this 
experiment. The current in 
amperes and the pressure in 
volts must be accurately 
read from instruments. From 
this experiment it was found 
that a current of 1 ampere 
flowing through the coil 
under a pressure of 1 volt (or 
1 watt expended) would do 
the same work as 0.7375 
foot-pound expended in 1 
second. The rates of work- 
ing are thus equal, since the 




Fig. 109. — Joule's Paddle-wheel 
Experiment. 



same work in each case has been accomplished in the same time. 
Therefore, 

1 watt = 0.7375 foot-pound per second, 
or 1 foot-pound per second = 1.356 watts. 

Now, since 550 foot-pounds per second are equivalent to 1 
mechanical horse power (H 139), an equivalent rate of elec- 
trical working would, therefore, be: 



550 
0.7375 



= 746 watts = 1 electrical horse power. 



A current of 1 ampere at 746 volts, or 746 amperes at 
1 volt, etc., maintained through the calorimeter coil for 1 
second would heat the water to exactly the same temperature 
that it would be heated by the paddle wheels when, in 1 
second, 550 pounds fall through a distance of 1 foot, or 1 
pound falls through 550 feet, etc. If these rates of working 
are continued for equal periods of time, as an hour, or a day, 
the water is raised to the same temperature by either method, 
so that the total work performed is also the same. 



ELECTRICAL WORK AND POWER 153 

146. Electrical Horse Power. — In H 145 the method of 
obtaining the equivalent of a mechanical horse power in elec- 
trical units was given. The watt being a very small unit of 
power, the larger unit, electrical horse power, is often used. 

To FIND THE ELECTRICAL HORSE POWER (H.P.) MAIN- 
TAINED IN ANY CIRCUIT, OR PART OF A CIRCUIT: 

Multiply the volts causing the current to flow by the current 
expressed in amperes and divide this product by 746. 

TT p - ^^^^^ volts X amperes _ E x I ,-_x 

' * ^ 746~ ^ 746 ^ 746 ' ' ' ^ ^' 

Problem 75. — A generator maintains a pressure of 110 volts across an 
electric-light circuit, and the ammeter indicates 100 amperes; what horse 
power is being developed by the machine? 

-D T? 1 /Ir^^ XT 13 EXI 110X100 .,^XTT> 

By Formula (57) H. P. = = = 14.7 H. P. 

746 746 

147. The Kilowatt. — The kilowatt (abbreviated kw.) is 
a larger unit of electrical power. One kilowatt equals 1000 
watts, or is about 1\ times as large as the horse power unit. 

Kilowatts (kw.) = ^^^^ = E_x_I 

^ ^ 1000 1000 ^ ^ 

Watts = kw. X 1000 . , (59). 

1 H. P. = 0.746 kw. 
1 kw. = 1.34 H. P. 

Problem 76. — What is the capacity in kilowatts of a generator carrying 
a load of 500 amperes at 120 volts? 

r> TT 1 fKO\ 1 E X I 120 X 500 „„ , 

By Formula (58) kw. = = = 60 kw. 

^ 1000 1000 

Problem 77. — How many amperes will be maintained by a 40-kw. 
generator at a pressure of 100 volts? 

By Formula (59) Watts = kw x 1000 = 40 x 1000 = 40,000 watts. 

T^ T- 1 rrrs T P 40000 ,^^ 

By Formula (55) I = — = = 400 amperes. 

148. The Watt-hour and Kilowatt-hour. — The joule is 
a very small unit of electrical energy or work, so that larger 
units are generally used in practice. A watt-hour is one watt 



154 LESSONS IN PRACTICAL ELECTRICITY 

exerted or expended for one hour. It is equivalent to 3600 
watt-seconds (or joules) or also to 60 watt-minutes. 

Watt-hours = watt x hours. 

The dials of consumer's meters, used to measure the elec- 
trical energy supplied for lighting and power, generally record 
watt-hours, ^ 226. A kilowatt-hour is a larger unit of electrical 
work and is equal to 1000 watts or 1 kw. maintained for one 
hour, or 500 watts maintained for two hours, etc. 

Kilowatt-hours = kw. X hours. 

An electrical horse-power-hour is one electrical horse power 
maintained for one hour, or 746 watts maintained for one 
hour. 

Horse-power-hours = H. P. x hours. 

Electrical energy is generally supplied from stations at a 
fixed rate per horse-power-hour or kilowatt-hour. The total 
cost of producing a kilowatt-hour varies with many station 
conditions; from about 1 to 7 cents per kilowatt-hour is the 
range in a number of plants. 

149. Electrical Power Calculations. — The following rules 
and formulae have been derived either by transposing the 
formulae in IJH 143 to 148, or by combining them with the 
formulae given in Lesson VIII, Ohm's Law. This lesson is 
very important in the solution of many practical problems. 
The formulae apply equally well to the whole, or any part 
of a circuit; as, for example, to the lead wires to a lamp 
as well as to the lamp itself, or the internal resistance of a 
battery or dynamo. Caution must be exercised to use the volts 
lost or drop, If 131, in the particular part of any circuit con- 
sidered, also the resistance of, and the current through, this part 
only. The symbols used to represent the quantities are as 
given heretofore. 

Case 1. — Given current and pressure, to find tfe 
WATTS expended: 

The watts lost or expended in any circuit equals the product of 
the current and the pressure causing it to flow, Formula (54). 

P = ExL 



ELECTRICAL WORK AND POWER 155 

Case 2. — Given current and resistance, to find the 

ENERGY EXPENDED IN WATTS: 

The watts lost or expended in any circuit are equal to the cur- 
rent squared multiplied by the resistance. This is often called the 
^' I-square R loss" . 

P = PxR . (60). 

This formula is obtained by substituting the value of 
E = I X R in Formula (54). 

Problem 78. — The resistance of the field magnets of a dynamo is 220 
ohms and the magnetizing current is 2 amperes. What energy is expended? 
By Formula (60) P = PR = 2 x 2 x 220 = 880 watts. 

Case 3. — Given resistance and pressure, to find the 
WATTS expended: 

The watts lost or expended in any circuit are equal to the square 
of the pressure divided by the resistance. 

E2 
P = R •••• ......(61). 

This formula is obtained by substituting the value of 

F 

I = — in Formula (54). 
R 

Problem 79. — The resistance of a telephone relay is 200 ohms. What 
power is expended in the relay when operated on 24 volts? What cur- 
rent does it take? 

F,2 94- V 94 
By Formula (61) P = — = "^ = 2.88 watts. 
•^ R 200 

By Formula (27) I = :^ = ^ = 0.12 ampere. 

Case 4. — Given watts expended and current, to find 
THE resistance: 

The resistance is equal to watts expended divided by the square 
of the current. 

R = | (62). 

This formula is found by transposing Formula (60). 



156 LESSONS IN PRACTICAL ELECTRICITY 

Problem 80. — A 55-watt incandescent lamp requires 0.5 ampere. What 
is its resistance? 

By Formula (62) R = - = — = ^^ =220 ohms. 

^ P 0.5 X 0.5 0.25 

Case 5. — Given watts expended and resistance, to 
FIND the current: 

The current equals the square root of the watts divided hy the 
resistance. 

=Vi •••• ''''■ 

This formula is obtained by transposing Formula (60). 

Problem 81. — If the hot resistance of a 55-watt lamp is 220 ohms, what 
current will it require? 

By Formula (63) I =^1 = ^^ = \Jl=l ^"^P^^^' 

Case 6. — Given watts expended and pressure, to find 
the resistance: 

The resistance equals the square of the pressure divided by the 
watts expended. 

R=^ ■ • (64). 

This formula is obtained by transposing Formula (61). 

Problem 82. — What is the resistance of a 55-watt, 110- volt incan- 
descent lamp? 

By Formula (64) R = — = ^^^ ^ ^^^ = 220 ohms. 

In the above formulae if the value of P is given in the larger unit of power, 
the horse power, or if it is desired to express its value in the larger unit, the 
formulae may he changed by remembering that 1 horse power = 746 watts. 

150. Power from Cells. — The amount of power that can 
be furnished by a cell is directly proportional to the square of 
its E. M. F. divided by its internal resistance and is equal to 
the number of watts expended by the cell on short-circuit. Let 
P represent the power in watts from a single cell, then from 
Formula (61) we get 

P = ^ • ^... (65). 

r 



ELECTRICAL WORK AND POWER 157 

The power obtained from any number of similar cells is 
equal to the power of one cell multiplied by that number, 
and is independent of the grouping, provided that it is sym- 
metrical. For example, the amount of power a dry cell can 
furnish, if the E. M. F. is 1.5 volts and internal resistance is 

E^ 15x15 
0.25 ohm, is P = — = ' ^ "^ — '— = 9 watts. The power furnished 
r 0.2o 

by ten cells would be 10 x 9 = 90 watts. 

If arranged all in series then the total E. M. F. = 15 volts 
and total internal resistance = 2.5 ohms, and 

^ E2 15x15 „„ .^ 

P = — = = 90 watts. 

r 2.5 

If arranged all in parallel, then the total E. M. F. = 1.5 volts 
and the internal resistance = 0.025, and 

P = ^ = — ^ = 90 watts, as before. 

r 0.025 

In the above cases all the energy is expended inside the cell, 
no external resistance being considered. 

151. Efficiency. — By efficiency is meant the relation of the 
useful work done to the total energy expended. The effi- 
ciency of a device is the ratio of energy delivered by it to the 
energy supplied to it. A perfect battery or generator (that is, 
one with no internal resistance) would deliver all of the energy 
to the external circuit, but as some portion of it is lost in the 
internal resistance the useful energy is always less than the 
total energy expended. The efficiency of a battery is the ratio 
of the external energy to the total energy developed, and this is 
the same as the ratio of the external to the total resistance in 
the circuit. If the total energy expended is represented by 
100, and one half of this amount is unavailable for useful work, 
the efficiency would be 50 per cent. 

To FIND THE EFFICIENCY OF A BATTERY: 

Divide the resistance of the external circuit by the resistance of 
the external circuit plus the resistance of the battery. 

Efficiency = -^ (66). 



158 LESSONS IN PRACTICAL ELECTRICITY 

Problem 83. — What is the efficiency of a battery dehvering current 
through an external resistance of 3 ohms when the battery resistance is 
3 ohms? 

By Formula (66) efficiency = — ^ = -^ = 0.50 or 50% 

Suppose the current furnished by the battery is 2 amperes, 
then the power expended in the external resistance will be 
P xK = 2^ X S = 12 watts; the internal resistance being of 
the same value as the external, the same amount of power 
is there expended, so that the efficiency is the ratio of 

useful watts 12 _ _ _ _ _ ^ , , 

— - = — = 0.50 = 50 %, as before. 

total watts expended 24 

Let P = useful energy expended in watts, 
p = useless energy expended in watts. 

Then, 

p 
efficiency = — (67). 

P + p 

QUESTIONS 

1. What is the difference between force and- work? 

2. Define mass, energy, power, weight. 

3. What is the unit (a) of mechanical power? (6) of mechanical 
work? (c) of electrical work? (d) of electrical power? 

4. Cite examples illustrating the conservation and correlation of 
energy. 

5. How would you ascertain, by experiments, the mechanical equiva- 
lent of work performed by an electric current? 

6. What is the difference between a kilowatt and a kilowatt-hour? 

7. A battery used in electroplating has an efficiency of 70 per cent. 
What do you understand by this statement? 

PROBLEMS 

1. How much electrical power is expended in illuminating a 16-candle 
power incandescent lamp, supposing "that it has a resistance of 220 ohms 
(hot) and is taking 0.5 ampere? How many watts per candle power? 
How many such lamps can be maintained at full candle power by one 
mechanical horse power? Arts. 55 watts; 3.43 watts; 13 lamps. 

2. A number of 100-volt incandescent lamps are being lighted by a 
generator having a P. D. of 112 volts at the brushes. The resistance of 
the leads carrying current to the lamps is 0.05 ohm. Each lamp requires 
50 watts. How many lamps are burning? Ans. 480 lamps. 



ELECTRICAL WORK AND POWER 159 

3. (a) What size of generator (kilowatt capacity) should be pur- 
chased for a 500-lamp installation, supposing that 50-watt incandescent 
lamps are to be adopted? (6) What would be the kw. capacity of a 
motor required to be substituted for a 25-horse-power gas engine? Ans. 
(a) 25 kw.; (6) 18.65 kw. 

4. In constructing a solenoid and core to actuate a lever, 500 feet of 
number 18 B. & S. copper magnet wire is wound upon a brass spool. A 
table of heating limits gives 4 amperes as a safe carrying capacity for 
this size of wire under these conditions. Using this current, how much 
extra resistance must be added to place the coil across a hne of 110 volts 
potential difference? Ans. 24.24 ohms. 

5. The above solenoid is to operate in series with the field magnets 
of a dynamo having 20 ohms resistance, (a) How much extra resistance 
must now be added to place the fields and coil in series across the above 
mains so as to receive the same current? (6) How many feet of No. 18 
B. & S. iron wire are required to construct a rheostat for the extra resist- 
ance in this problem? (c) How much energy is consumed in the solenoid? 
Ans. (a) 4.24 ohms; (5) 110 feet; (c) 52.1 watts. 

6. A street car is driven by two four-pole series motors. Each field 
magnet has a resistance of 0.125 ohm, the armature has 0.125 ohm and 
an extra rheostat has 4 ohms. The E. M. F. between trolley wire and 
rails is 500 volts. Neglecting the counter E. M. F. of the motors, find the 
current the motors will receive in the following positions of the controller 
switch: — (a) first point: both motors in series, all field coils in series, 
extra resistance in series. (6) fourth point: both motors in parallel and 
the extra resistance in series with them, (c) What power is the car receiv- 
ing on the fourth point? (d) Make' a sketch of both controller combina- 
tions. Ans. (a) 95.2 amperes; (6) 115.9 amperes; (c) 77.7 H. P. 

7. An electric automobile is equipped with 40 storage cell which are 
connected, through the controller switch, for the first speed, 20 cells in 
series and two groups in parallel. Each cell has an E. M. F. of 2 volts 
and an internal resistance of 0.1 ohm. The resistance of the motors, 
extra resistance and leads at this combination is 0.5 ohm. (a) What is 
the value of the current required to start the vehicle? (6) How much 
power is expended at the start? Ans. (a) 26.6 amperes; (5) 1064 watts. 

8. While visiting an electric fight station you note the following indica- 
tions of instruments on the switchboard: voltmeter 115, ammeter 330. 
The plant operates the two-wdre direct-current system. What is the 
load on the generator expressed in kilowatts and electrical horse power? 
Ans. 37.95 kw.; 50.87 H. P. 

9. A compound-wound generator is connected to a circuit to which 
the following apparatus is wired: 150 incandescent lamps, each requiring 
0.6 ampere; 3 arc lamps taking 10 amperes each; various electrical 
cooking and heating appliances requiring when all are at work 20.5 
amperes; two electroplating and electrotyping baths arranged in series 
across the mains and taking a maximum current of 5 amperes; 10 storage 
cells in series with a lamp-bank resistance across the mains and requir- 
ing a charging current of 10 amperes. The two-wire direct-current system 



160 LESSONS IN PRACTICAL ELECTRICITY 

is used and a constant potential difference of 110 volts is maintained be- 
tween the mains. What is the output of the generator in electrical horse 
power, supposing that the maximum current ever required is 75 per cent of 
that taken when the whole installation is in operation? Ans. 17.19 H. P. 

10. The mean effective steam pressure from an indicator card is 50 
pounds per sq. in.; the speed of the engine is 290 revolutions per minute; 
the length of stroke is 10 inches; the area of piston head is 0.75 square 
foot. What horse power is developed by the engine? Ans. 78.77 H. P. 

11. What is the current flowing through an electromagnet having a 
resistance of 50 ohms and requiring 200 watts? Ans. 2 amperes. 

12. What is the maximum power obtainable from a Grenet cell of 2 
volts E. M. F. which has an internal resistance of 0.02 ohm? Am. 200 
watts. 

13. (a) What is the efficiency of a battery of 34 cells in series delivering 
current to four 50-volt, 50-watt incandescent lamps (resistance assumed 
constant) in parallel? Each cell has an E. M. F. of 2 volts and an internal 
resistance of 0.1 ohm. (6) What power is expended in the battery? 
Ans. (a) 78%; (6) 54.4 watts. 



LESSON XII 

STORAGE BATTERIES 

The Storage or Secondary Cell — Direction of Current in a Storage 
Battery on Charge and Discharge — Chemical Action in a Lead 
Storage Cell — The Electrolyte in a Lead Cell — The Hydrometer 

— The Voltage of a Lead Storage Cell — Types of Lead Plates used 
in Storage Cells — The Rated Capacity of a Storage Cell or Battery 

— Care and ' Maintenance of Lead Cells — The Nickel- Alkah or 
Edison Storage Cell — Efficiency of a Storage Cell — Methods of 
Charging — Uses of Storage Batteries — Questions. 

152. The Storage or Secondary Cell. — A storage cell is a 
voltaic cell consisting of two plates of metals or metallic com- 
pounds immersed in an electrolyte, the materials of the plates 
and electrolyte being so chosen that the cell, after having 
delivered an electric current for a certain time, may be restored 
to its original condition in a simple and efficient manner. This 
restoration is accomplished by sending a current from an 
outside source of electricity through the cell in a direction 
opposite to that of the current supplied by the cell; this process 
is called charging. When the cell delivers current to an 
external circuit it is said to be discharging. 

The difference between a primary cell and a secondary cell 
is as follows: The primary cell consists of two dissimilar plates 
and an electrolyte that will act chemically on the positive 
plate (zinc) when the external circuit is closed, thereby convert- 
ing the chemical energy of the cell into an electric current. 
When the zinc is almost consmned, it is replaced with a new 
one and fresh electrolyte is added in order to restore the cell 
to its initial condition. In a secondary cell the plates arid 
electrolyte are of such materials that there is no chemical 
action between them until after a current has first been sent 
through the cell; that is, the cell must first have been charged. 
As the materials become exhausted in discharging the cell, 
they are capable of being renewed by the passage of an electric 

161 



162 LESSONS IN PRACTICAL ELECTRICITY 

current through the cell in a direction opposite to that of the 
current on discharge. Charging a storage cell means that the 
electrical energy supplied to it is converted into chemical 
energy which is stored in the cell, and discharging means that 
this chemical energy is transformed back again to electrical 
energy in maintaining a current through an external circuit. 
When two or more storage cells are electrically connected 
(usually in series) they form a storage battery, or secondary 
battery, or accumulator. 

Experiment 55. — Place two copper strips in a solution of zinc sulphate 
contained in a small battery jar. Connect the terminals of the copper 
strips to a galvanometer, and note that the needle is not deflected, because 
the combination does not conform to the definition of a voltaic cell, ^j 29. 
Disconnect, and substitute for the galvanometer two bichromate cells 
connected in series. By electrolysis, part of the zinc sulphate (ZnS04) 
is converted into sulphuric acid (H2SO4), and metallic zinc is deposited on 
one of the copper plates. After the action has taken place for a little 
while, disconnect the battery and again connect the electrolytic cell to 
the galvanometer, and note that its needle is now deflected. 

No electricity was stored in Experiment 55, but a chemical 
action took place, which changed the plates into two dissimilar 
metals and the salt (zinc sulphate) into an acid capable of 
attacking one of them, thus conforming to the definition of a 
primary cell. The chemical action on discharge of this simple 
type of accumulator will be obviously the same as in the voltaic 
cell of II 36, since the plates (copper and zinc) and the acid (sul- 
phuric) are identical with those of that cell. On discharge the 
zinc is consumed by the acid, and when it is all dissolved in 
the solution the cell is entirely discharged and must be re- 
charged again by electrolysis. 

Experiment 56. — Place two lead strips in the U-tube (Fig. 70), fill 
with acidulated water, and connect the plates to a detector galvanometer. 
No deflection is noted. Now connect the plates to two bichromate cells 
(in series), and after passing a current for a short time examine the plates, 
and you will find that the positive plate has become brownish in color, 
while the negative plate is lighter in color. Connect the plates to the 
galvanometer, and note that the needle indicates the discharging current. 

Lead plates in dilute sulphuric acid were first used by Plante, 
from whom this type of cell takes its name. The charging 
action just described changes the positive lead (Pb) plate to 



STORAGE BATTERIES 163 

lead peroxide (PbOa), while the negative plate is left in the form 
of spongy lead. On discharging the ceU both the peroxide 
plate and the lead plate are gradually reduced to lead sulphate 
(PbS04), which forms a whitish coating on the plates. The 
positive and negative plates are readily distinguished by their 
color — the positive is a dark brown and the negative a light 
gray. 

153. Direction of Current in a Storage Battery on Charge 
and Discharge. — Upon charging the cell in Experiment 55, 
the direction of current inside the cell was from copper to 
zinc; upon discharge, the current inside the cell travels in 
the opposite direction (zinc to copper, as in a voltaic cell). In 
Experiment 56, the direction of the charging current inside 
the cell was from the positive (lead plate) to the negative (lead 
plate); upon discharge the current was from the terminal of 
the positive (lead peroxide) plate through the galvanometer 
to the negative-plate terminal, and from the negative plate 
to the positive plate inside the cell. Consequently the positive 
terminal of a storage battery must be connected to the positive 
terminal of the charging lines, in order that this same terminal 
will again be positive on discharge. 

There are two kinds of storage batteries in use, namely: the 
lead-acid battery, and the nickel-alkali or Edison battery. 
The lead cell will be considered first. 

154. Chemical Action in a Lead Storage Cell. — Referring 
again to Experiment 56, it will be recalled that when the cell 
was in a charged condition the positive plate was lead peroxide 
(Pb02), and the negative plate was spongy lead (Pb). These 
plates are the active materials of commercial lead-acid storage 
batteries, and the electrolyte is a solution of sulphuric acid 
(H2SO4) and water (H2O). When such a storage cell is dis- 
charging, the current which is in the direction from the negative 
plate to the positive plate inside the cell breaks up the elec- 
trolyte into hydrogen (H2), which goes to the positive plate, 
and the radical SO4, which travels to the negative or sponge, 
lead plate. At the latter electrode, the radical SO4, unites 
directly with the sponge lead to form lead sulphate (PbS04). 
The hydrogen which is liberated at the positive or lead peroxide 
plate, together with some hydrogen derived from sulphuric 



164 LESSONS IN PRACTICAL ELECTRICITY 

acid in contact with that plate, unites with the oxygen of the 
lead peroxide and forms water. The SO4 of the latter acid 
unites with the lead of the lead peroxide plate and changes it 
to lead sulphate (PbS04). Thus both plates are gradually 
converted into lead sulphate. If both plates were reduced 
entirely to lead sulphate the cell would no longer deliver 
current, for there would then be but one kind of material 
present, and a battery must have two dissimilar materials. 
In practice, the discharge of a lead cell is not continued until 
both plates are completely reduced to lead sulphate, because 
lead sulphate has (1) a very high electrical resistance, and 
(2) is more bulky than the active material. Because of its 
greater bulk, the sulphate clogs up the space occupied by the 
active material in the plates and if excessive tends to ''buckle" 
or warp them. 

Assuming, however, that both plates have been completely 
reduced to lead sulphate by a full discharge of the cell, and a 
current from an outside source is then sent through for charging 
it, the chemical action is as follows: The charging current 
breaks up the water, which was formed during the discharge, 
into hydrogen and oxygen gas. The hydrogen is liberated at 
the negative plate, where it unites with the SO4 of the lead 
sulphate (PbS04) to form sulphuric acid (H2SO4), and leaving 
pure spongy lead. The oxygen liberated at the positive plate, 
together with some oxygen from water in solution, unites with 
the lead of the lead sulphate, and forms lead peroxide (Pb02). 
The SO4 radical of the positive plate enters into chemical 
union with the hydrogen hberated from. the water and forms 
sulphuric acid (H2SO4). When the positive and negative 
plates have been completely converted respectively into lead 
peroxide and pure lead, the battery is back in its condition 
prior to discharge, and is again ready to supply current. The 
foregoing chemical actions on discharge and charge of a lead 
cell may be represented by the following equations in which 
the electrolytes are indicated by braces: 

Discharge 

Positive Pb02 + [^2 \ + H2SO4 = PbS04 + 2 H2O 
Negative Pb + VSO4/ = PbS04 



STORAGE BATTERIES 165 

Charge 

Positive PbS04 + /O \ + H2O = PbOa + H2SO4 
Negative PbS04 + \ii2J = Pb + H2SO4. 

These four equations may be collected into a single expression 
as below 

Both plates Pb02 + Pb + 2 H2SO4 :^ 2 PbS04 + 2 HaO. 

Reading the last equation from left to right the reactions are 
those which take place on discharge, while reading from right 
to left the reactions are those accompanying charge of a lead 
storage cell. 

155. The Electrolyte in a Lead Cell. — The liquid in a 
lead storage cell is a solution of sulphuric acid and water, the 
percentage of acid varying from 22 to 37 % by volume depend- 
ing on the type of cell. It is important to have the electrolyte 
of the right strength or the cell will not function properly. 
The concentration of the electrolyte, or the proportion of acid 
to water, can best be determined from measurements of its 
specific gravity. The specific gravity of a liquid is a measure 
of its density or weight per unit of volume as compared with 
that of chemically pure water. If the density of water be 
taken as unity (or 1), it is found that solutions of acid, etc., 
are heavier than water or have a density exceeding unity. 
Thus the specific gravity of the electrolyte of one type of lead 
storage cell is approximately 1.2, which means that if a cubic 
centimeter of water weighs one gram, one cubic centimeter 
of the electrolyte will weigh 1.2 grams. The greater the 
proportion of acid in the electrolyte of a storage cell, the higher 
will be the reading of its specific gravity. The specific gravity 
of pure sulphuric acid is 1.835 (at 60° F.). It is quite common 
in dealing with storage batteries to call the specific gravity of 
water 1000 rather than unity; then the foregoing electrolyte 
would have a specific gravity of 1200. 

The electrolyte should be made of either distilled or rain 
water mixed with chemically pure concentrated sulphuric acid. 
The proportion of water differs with several types of cell from 
2.5 to 5 parts of water by volume to 1 part of acid, as specified 
in the directions suppHed by the manufacturer with the cells. 



166 LESSONS IN PRACTICAL ELECTRICITY 

The proper specific gravity for a cell depends somewhat upon 
the use for which it is intended. A cell under continuous 
operation may have a higher density than one which frequently 
stands unused for long intervals of time. In the latter case, 
the use of strong acid would change the active material into 
lead sulphate when standing idle more rapidly than if weaker 
acid were used. It is, however, of advantage to employ as 
high" a density as practicable, for then the cell will have a low 
internal resistance and yield a high E. M. F. To make elec- 
trolytes of the proper specific gravity for use in lead storage 
batteries, the following proportions hy volume of pure water 
to one part of acid are used: 

Density Sulphuric Acid Water 

1200 1 part 4.3 parts 

1250 1 part 3.2 parts 

1275 1 part 2.8 parts 

1300 1 part 2.5 parts 

Acid must always he poured into the water, preferably in a glass, 
china, or earthenware vessel, and must be allowed to cool 
before specific gravity readings are made. 

The acid of a lead storage cell becomes weaker during dis- 
charge of the cell, and stronger as the cell is recharged. This 
fact is displayed by the equations of If 154, since sulphuric 
acid is replaced by water during discharge, and vice versa. 
The condition of a cell, with regard to charge or discharge, is 
then readily ascertained by testing the specific gravity of its 
electrolyte, which test is conveniently made with a hydrom- 
eter, U 156. When fully charged the electrolyte should have 
a specific gravity of from 1200 to 1280, according to the class 
of work for which the cell is intended. On discharge the* 
specific gravity should never fall below 1175. 

156. The Hydrometer. — The density or specific gravity of 
the electrolyte in a storage cell is measured by an instrument 
known as a hydrometer. One type is illustrated in Fig. 110, 
and consists of a long glass tube, near the bottom of which 
are two bulbs. The lower and smaller bulb is loaded with 
mercury or shot so as to cause the instrument to float in a 
vertical position when placed in the hquid. The upper bulb is 
filled with air and its volume is such that the whole instrument 



STORAGE BATTERIES 



167 



is lighter than an equal volume of water. There is a graduated 
scale placed inside the upper part of the glass 
tube. When dropped into a solution of acid, 
the hydrometer sinks to a certain depth, de- 
pending upon the density of the liquid. The 
reading of the hydrometer scale at the siuf ace of 
the solution is a measure of its specific gravity. 
In the large storage batteries used in central 
stations there is sufficient room in the cells to 
float the hydrometer in their electrolytes. But 
in using this instrument (Fig. 110) to test the 
electrolyte in a portable storage cell, enough 
liquid would have to be transferred to a sepa- 
rate glass jar to float the hydrometer. A more 
convenient instrument for this purpose, and 
one that is extensively used for testing the con- 
dition of storage batteries used on automobiles, 
is shown in Fig. 111. It consists of a small 
hydrometer within a glass-barrel syringe, which 
has a rubber bulb at its upper end for drawing 

enough liquid into the glass barrel to float the Fig. 110. — Acid 
1 J , Hydrometer, 

hydrometer. • -^ 

157. The Voltage of a Lead Storage Cell. — The voltage of 

a storage cell does not depend upon the size of the cell, but 

does depend upon the character of the electrodes, the specific 

gravity of the electrolyte, and the condition of charge. The 





Fig. 111. — Hydrometer Syringe. 

volt a of a lead storage cell is roughly 2 volts. While being 
charged, its voltage is from 2.0 to 2.6 volts, increasing as the 
charge progresses. As the battery discharges, the voltage 
gradually decreases, from about 2.1 to 1.7 volts. 

The fall in voltage on discharge is due to the weakening of 
the electrolyte and to the changing of the pure active materials 
into a mixture of active material and lead sulphate ; the f orma-= 
tion of the latter increases the internal resistance of the cell, 



168 LESSONS IN PRACTICAL ELECTRICITY 

and the surface layer of lead sulphate prevents access of the 

electrolyte to the interior pores of the active material. It is 

good practice not to discharge the cell below 1.8 volts, and if 

the discharge is carried to that point a charging current should 

be sent through the cell within a reasonable time, for if a cell 

is discharged to that voltage and the plates are left to stand 

in the acid, further sulphating will take place rapidly. The 

limiting voltage beyond which discharge should not be carried 

depends upon the rapidity of discharge. The value of 1.8 

volts above given applies to the so-called "normal" discharge 

rate, H 159; if the discharge of an emergency battery takes 

place in one hour the voltage may safely be allowed to fall to 

1.6 volts. 

158. Types of Lead Plates Used in Storage Cells. — In all 

lead-acid storage cells, as stated in H 154, the active materials 

are lead peroxide at the positive 

/^^~ plate and sponge lead at the nega- 

^ tive plate. These active materials 

have no mechanical strength, and 

therefore in order to make them 

into suitable plates it is necessary 

that they be supported in frames 

or grids. These grids are usually of 

. ^ lead-antimony alloy, which is an 

alloy not attacked by the sulphuric 

acid electrolyte; therefore no local 

action occurs. In the production of 

i7- 110 .(Ti/r u u. n battery plates there are two general 

Fig. 112. — "Manchester" 4.^: di ,- j- j. j 

Positive Plate. types, the Flante or jormea type and 

the Faure or pasted type. 

In the Plant e type of plate the active materials are formed 

on the surfaces of the plates by chemical or electro-chemical 

means from the lead plates themselves. Since the layer of 

active material produced in this way is relatively thin, the 

production of a sufficiently large quantity to render each 

plate of suitable capacity demands that the area exposed to the 

electrolyte be as large as possible. This increased surface is 

procured by making grooves or ribs in the plate, or by making 

up the plate of long narrow ribbons of lead which are folded 




STORAGE BATTERIES 



169 




Fiff. 113. 



"Tudor' 
Plate. 



Positive 



in various ways to form a plate of thickness equal to the width 
of the ribbon. The Manchester form of Plante plate (Fig. 112), 
manufactured by the Electric Storage Battery Company, 
consists of a grid cast of lead-anti- 
mony in which are a number of 
circular holes f inch in diameter. 
Soft corrugated pure lead ribbon 
is rolled into spiral buttons or 
'^rosettes" and forced into the 
holes of the grid by hydraulic 
pressure, which securely locks them 
in position. During the forming 
process the buttons expand, thus 
improving the electrical contact. 
The Tudor form of Plante plate 
(Fig. 113), also manufactured by 
the Electric Storage Battery Co., 
is a cast plate, consisting of a 
single piece of lead with a number of vertical ribs extending 
^^ from face to face, allowing thor- 

'ttk ough circulation of the electrolyte 

^■B ^^ through the narrow spaces. At 

Bv_ JH suitable intervals these ribs are 

r "^H supported by horizontal ribs to 

insure proper rigidity. The Gould 
plate, made by the Gould Storage 
Battery Company, is ''spun" from 
a sheet of lead by passing it back 
and forth between revolving man- 
drels, each having many steel discs 
at short intervals; thus forming a 
large exposed surface in proportion 
to its size. The Plante type of 
plate is used chiefly for positives; 
only the Gould plate is in general use in this country as a nega- 
tive true Plante plate. 

In the Faure or pasted type of plate, the active material 
in paste form is spread on the surface of the plate or placed in 
the apertures of the grid. The paste masses used in practice 



Fig. 114.- — "Pasted" Negative 
Plate. 



170 



LESSONS IN PRACTICAL ELECTRICITY 




Fig. 115. — "Box" Negative 
Plate. 



utilize the cementing action which results from the formation 

of lead sulphate to harden the paste. The original pasted 

plate as developed by Faure con- 
sisted of thin sheets of lead, rough- 
ened on their surface, over which 
was spread the active material. 
This method was not commercially 
successful because the active mater- 
ial, the lead peroxide on the positive 
plate, did not adhere thoroughly to 
the supporting grid and fell away. 
Many forms of grid for locking the 
material have been developed ; they 
consist of antimony-lead castings of 
various patterns, such as the ''shelf " 
and "diamond" type. Fig. 114 
shows a pasted plate. Such plates 

are principally used where the greatest 

capacity is desired for minimum 

weight and space. The box negative 

plate (Fig. 115) consists of an alloy 

frame with a number of small openings 

which are filled with finely divided 

porous sponge lead. As this material 

is not mechanically self-supporting, a 

perforated cover is placed on each side 

of the frame to hold the blocks of 

active material in place. 

A combination of the Faure negative 

plate and the Plante positive plate is 

found in the "Chloride Accumulator" 

(Fig. 116) made by the Electric Storage 

Battery Co., which consists of a Man- 
chester positive and a box negative. 

The Chloride Accumulator, as made at 

the present time, is "Chloride" in 




Fig. 116. —"Chloride' 
Accumulator. 



name only, as the active material is 
not made from chlorides, as it was in 
the original Chloride Battery manufactured at one time by 



STORAGE BATTERIES 



171 



JL VL-pM 



i 



that and allied companies abroad. This well-known trade 
name has been retained, though the method of manufacturing 
the present type of plates is entirely different. 

The Gould cell, made by the Gould Storage Battery Co., 
for heavy duty, as for power-station service, is an example of 
one using the Plante type 
of plate for both positives 
and negatives. 

The ''Exide Battery "is 
manufactured by the Elec- 
tric Storage Battery Co. 
chiefly for electric vehicle 
work and for starting, 
lighting and ignition ser- 
vice on automobiles. The 
positive and negative 
plates are of the Faure 




Positive Plate 



Negative Plate. 



Fig. 117. — Plates of an Exide Storage 
Cell. 



type, and consist of lead-antimony grids which support the 
active material in the form of a series of vertical strips held 

between the grid bars and 
locked in place by horizontal 
surface ribs that are staggered 
in opposite sides. After the 
grids are cast, they are '* pasted " 
with oxides of lead made into 
a past ) of special composition 
which sets in drying. The 
plates then go through an elec- 
tro-chemical process which con- 
verts the material of the posi- 
tives into brown peroxide of 
lead and that of the negative 
into gray spongy lead. Fig. 117 
shows a finished positive and 
negative plate; Fig. 118 shows 
a complete Exide element. One 
of the chief features of this 
batter}^ is increased power for 
a given weight and size, which is obtained by the use of thin 




Fig. 118 — Complete Element- 
Exide Storage Cell. 



172 



LESSONS IN PRACTICAL ELECTRICITY 



plates of large area, yet so designed as to be rugged and long- 
lived. 

The ''Ironclad-Exide Battery" (Fig. 119), used principally 
for the propulsion of vehicles, is an improvement on the Exide 
battery in the method of holding the active material in the 
positive plate. This plate has a grid composed of a number of 

parallel vertical metal rods which are 
united integrally to horizontal top and 
bottom frames, the frame being pro- 
vided with the usual conducting lug. 
Each vertical rod forms a core which 
is surrounded by a cylindrical pencil of 
peroxide of lead, the active material. 
This, in turn, is inclosed by a hard 
rubber tube having a large number of 
horizontal slits. These slits serve to 
provide access for the electrolyte to 
the active material, and yet are so fine 
as to practically eliminate the wash- 
ing out of the material. The Ironclad- 
Exide negative plate is of modified 
Exide form ; the top and bottom edges 
are encased in rubber, vulcanized in 
place. This arrangement eliminates 
the possibility of short-circuits from 
material bridging across from the posi- 
tive frames. 

159. The Rated Capacity of a Stor- 
age Cell or Battery. — The capacity 
of a storage cell is rated in ampere-hours, H 94, which is the 
quantity of electricity the battery v/ill supply from a fully- 
charged condition when discharging at constant current for 
a prescribed time until its voltage has fallen to a certain 
value. This rating is frequently based on the so-called normal 
or 8-hour rate of discharge for the stationary tj^pe of lead- 
acid batteries, other types being generally based on a shorter 
discharge. For example, if a cell is rated as having a capacity 
of 200 ampere-hours, its normal rate of discharge is deter- 
mined by simply dividing the rating 200 by 8, with the 




Fig. 119. — Iron-clad Exide 
Battery. 



STORAGE BATTERIES 173 

result that the normal current that can be taken from the 
cell is 25 amperes for 8 hours. Theoretically it would seem 
that this cell should give a discharge of 50 amperes for 4 hours 
or perhaps 200 amperes for one hour. Practical experience, 
however, has shown that if the rate of discharge of a cell is 
increased its ampere-hour capacity will' be decreased; thus 
the foregoing cell may only deliver 100 amperes at the one- 
hour rate. This reduction of capacity results from the in- 
ability of the acid to diffuse into the active material during 
quick discharges. At present there are many uses for storage 
batteries in which the time of discharge is much shorter than 
the normal 8-hour rate, and because the capacity varies with 
the discharge -rate, it is now the custom of battery manufac- 
turers to state the discharge current for various times. Thus a 
21-plate Type F cell made by the Electric Storage Battery Com- 
pany is rated to give 100 amperes for 8 hours, 140 amperes for 5 
hours, 200 amperes for 3 hours and 400 amperes for 1 hour. 

The capacity of a storage cell increases directly with the 
area of the plates exposed to the electrolyte. The capacity 
in practice is rated at from 40 to 60 ampere-hours (8-hour rate) 
per sq. ft. of exposed positive plate surface. Each cell of a 
storage battery of large capacity contains a number of positive 
and of negative plates. The positives are all connected to- 
gether in one group to a common terminal by means of a lead 
strap, and -the negative plates are connected in a similar group, 
as in Fig. 118, the two sets of plates being interleaved with 
each other, so that each positive plate has a negative plate 
adjacent to and facing it on either side. This requires one 
more negative plate in each cell than positives. 

Problem 84. — Allowing 50 ampere-hours per square foot of positive 
plate surface, what is the capacity of a lead storage cell which has 12 
positive and 13 negative plates, each 15 x 16 inches? 

Area of positive plates = 12 x 2 x 15 x 16 = 5760 sq. in. = 40 sq. ft. 

Capacity of cell = 50 x 40 = 2000 ampere-hours (8-hour rate). 

When the positive and negative groups are assembled to- 
gether, the adjacent plates, being of opposite polarity, must be 
kept separated and insulated from each other, as electrical con- 
tact between the two groups at any point will short-circuit the 
entire cell. For this reason separators are placed between 



174 LESSONS IN PRACTICAL ELECTRICITY 

the plates to prevent contact between them, and these sepa- 
rators are now almost universally made of wood. The positive 
and negative groups, together with the separators, are collec- 
tively called the element (Fig. 118); the element is usually set 
vertically in a containing jar of hard rubber or glass, or in a 
lead-lined wood tank. 

160. Care and Maintenance of Lead Cells. — The greatest 
care should be exercised in the maintenance and operation of 
storage batteries, for without proper care they deteriorate 
very rapidly. The main points to be considered in the opera- 
tion of lead cells are: (a) the electrolyte; (5) rates and extent 
of charge and discharge. 

(a) Only pure sulphuric acid and distilled w^ter should be 
used in making the electrolyte. If the electrolyte contains 
other acids or small amounts of any metals but lead, the 
battery will be subject to local action, and complex chemical 
reactions will go on which may ruin the cells. Impurities 
may be introduced by using ordinary faucet or well water in 
filling cells, or by allowing metal particles to get into them. 
The specific gravity of the electrolyte should be kept at the 
figure prescribed by the manufacturer; it will probably be in 
the neighborhood of 1210 for the stationary types and of 1280 
for the motor-vehicle types of cells when charged. Keep the 
level of the electrolyte above the tops of plates by filhng with 
pure water to make up for evaporation. Never add pure 
sulphuric acid. 

(b) It has been stated in If 159 that the more rapid the 
discharge of a storage cell the lower will be its ampere-hour 
capacity. Properly constructed Plante plates may be dis- 
charged at almost any rate without harm if they are charged 
again immediately after the completion of the discharge. 
Avoid overdischarge, as this produces an excess of lead sulphate 
in the deeper crevices of the plates and may occasion buckling 
or fracture. Buckled plates should be straightened out as 
soon as observed. Tests of terminal voltage of the cell and of 
specific gravity of the electrolyte will indicate when the cell 
has been discharged as much as is practicable; discharge 
should be discontinued when the voltage falls to from 1.8 to 1.6 
volts, and when the specific gravity has been lowered to from 



STORAGE BATTERIES 175 

1175 to 1185. Do not let the battery stand in an uncharged 
condition. 

Charging of storage batteries is usually carried out at higher 
rates than the normal 8-hour rate; for example, a cell has its 
charge started with a current value corresponding to the 3-hour 
discharge rate, and finished with a current corresponding to 
the 8-hour rate. Recent rules in regard to charging indicate 
that well-built lead cells in good condition may be charged 
at any convenient rate provided that their temperature does 
not exceed 105" or 110° F., and that they do not produce an 
excessive amount of gassing at the end of the charge. Insuffi- 
cient charging and charging at low rates are to he avoided; exces- 
sive sulphation and buckling of the plates may result otherwise. 
The charging of a battery should continue until (1) all its cells 
are gassing uniformly at both sets of plates, (2) the density of 
the electrolytes has reached its proper value for full charge, 
between 1200 and 1300, and (3) with constant charging current 
the voltage per cell does not rise further as determined by 
successive 15-minute readings. The voltage of a cell on open- 
circuit is of no value whatever in determining its condition of 
charge or discharge; voltage readings should be taken when 
the cell is either charging or discharging. An overcharge should 
be given to a storage battery weekly, biweekly or monthly, 
depending upon the nature of its work, the duration of this 
overcharge being at least one hour at the 8-hour charging rate. 
Indiscriminate overcharge is merely a waste of electrical energy, 
used only in producing gases. 

Cells should be kept clean. Active materials shed or fall 
away from the plates and accumulate in the bottom of the 
tank. Care must be exercised that this deposit does not rise 
high enough to touch and thereby short-circuit the plates. 
Keep the separators between the plates in good order. 

The constant inspection and care of a storage battery is 
well repaid by its increased life. Positive plates should last 
from three to ten years or longer, depending on service; nega- 
tives last much longer. 

161. The Nickel-Alkali or Edison Storage Cell. — The 
Edison Storage Cell is quite different from the lead-acid cells 
in electrolyte, active materials, and construction. The posi- 



176 



LESSONS IN PRACTICAL ELECTRICITY 




tive plate (Fig. 120) of the Edison cell consists of hollow per- 
forated tubes formed of spirally-wound steel ribbon. These 
tubes are filled with alternate layers of 
nickel hydrate and pure nickel flake; the 
nickel hydrate is converted to nickel oxide 
on first charge and this is the active 
material, the pure nickel in very thin 
flakes being introduced to increase the 
electrical conductivity. These tubes are 
firmly clamped into a steel supporting 
grid. The negative plate (Fig. 120) con- 
sists of perforated rectangular, sheet-steel 
pockets, which are loaded with iron oxide 
mixed with a httle mercury oxide to in- 
crease its conductivity. These pockets 
are placed in the apertures of the steel 
supporting grid and forced into good 
electrical contact 
under hydraulic 
pressure. Fig. 121 
shows the plates 
assembled into a complete element. All 
metallic parts are heavily nickel-plated, 
and the container is a rectangular vessel 
of sheet steel, nickel-plated. The elec- 
trolyte is a 21-per-cent solution of caustic 
potash, to which is added a small amount 
of lithium hydrate ; its density when made 
is from 1.20 to 1.23. 

The fundamental principle of the Edi- 
son cell is the oxidation and reduction of 
metals in an electrolyte which will not dis- 
solve or combine with either the metals 
or the oxides. The electrolyte is decom- 
posed by the current but is simultaneously 
reformed to an equal amount by a sec- 
ondary action, and it remains, therefore, 



Fig. 120. — Plates of 
the Nickel-alkali or 
Edison Storage Cell. 

Positive plate in front, nega- 
tive in back. 




Fig. 121. — Complete 
Element of the Edison 



practically constant in density and con- 



Storage Cell. 



ductivity over long periods of time, thus doing away with the 



STORAGE BATTERIES 177 

taking of hydrometer readings for determining the condition 
of the cell. 

When a charging current is first passed through the cell, the 
nickel hydrate is changed to nickel oxide, by the oxygen that 
is liberated acting on the positive plate, and the iron oxide is 
reduced to metallic iron, by the action of the liberated hydrogen 
upon the iron oxide; thus the cell may be considered to consist 
of a positive plate of nickel oxide (Ni02) and a negative plate 
of pure iron (Fe). During discharge of the cell the electrolyte 
of caustic potash (KOH) is broken up, the potassium (K) going 
to the nickel oxide and reducing it to a lower oxide of nickel 
(Ni304); the pure iron is changed to iron oxide (Fe304) by the 
Hberated OH uniting with the iron. Upon again sending a 
charging current through the cell the plates are brought back 
to their original conditions. These chemical actions may be 
represented by the following equations: 

Discharge 

Positive 6 Ni02 + o f K ] + 4 H2O = 2 Ni304 + 8 KOH 
Negative 3 Fe + I OH J = Fe304 + 4 H2O 

Charge 

Positive 2 Ni304 + ^ f OH ] =6 NiOs + 4 H2O 

Negative Fe304 + I K J + 4 HoO = 3 Fe + 8 KOH 

These four equations may be collected in a single expression 
as below, reading toward the right for charging conditions and 
toward the left for discharge. 

2 Ni304+Fe304+8 KOH+4 H20;=±6 Ni02+3 Fe+8 KOH+4 H2O. 

The average voltage of the Edison cell during discharge is 
1.2 volts, as against 2 volts of the lead-acid cell. Its cost is 
about twice that of the lead cell. These disadvantages, how^- 
ever, are offset by its ruggedness, lighter weight, great relia- 
bility, and low maintenance cost, particularly for certain 
classes of service, such as electric-vehicle propulsion and in 
train-lighting service. It will suffer no damage from subjection 
to such low temperatures as 40 degrees below zero F. The 
plates of the Edison battery will not be injured if allowed to 



178 LESSONS IN PRACTICAL ELECTRICITY 

stand for long periods in the electrolyte in a discharged condi- 
tion. The cell should be recharged when its voltage has fallen 
to 0.9 volt. Evaporation of the electrolyte is compensated 
for by the addition of distilled water. It may be fully charged 
at high rates without injury. 

162. Efficiency of a Storage Cell. ~ Not all of the electrical 
energy that is imparted to a storage cell during charge is 
recovered when it is discharged. The ratio between the 
energy in watt-hours taken out of a cell on discharge to the 
energy supplied to it on charge to bring it back to its original 
condition is termed its watt-hour efficiency (see ][ 151). This 
efficiency for the lead storage battery is about 70 to 80 per 
cent and for the Edison battery is about 60 per cent. The 
efficiency of batteries which discharge only partially and for 
short periods, and which are then again charged, may exceed 
the foregoing values. 

The efficiency of a storage cell may also be expressed by 
dividing the ampere-hour output by the ampere-hour input, 
which result is termed the ampere-hour efficiency. This effi- 
ciency, which is always higher than the watt-hour efficiency, 
may be as high as 90 or 95 per cent, for current is lost only by 
local action and by gassing at the ends of charge. Of the two 
efficiencies, the former or watt-hour efficiency is of commercial 
importance since it considers the energy relations, and includes 
the voltage as well as the ampere-hours. The watt-hour 
efficiency is lower than the ampere-hour efficiency, due to the 
fact that the E. M. F. on charge is higher than on discharge. 

Problem 85. — A storage battery comprising 50 series-connected cells 
is charged at an average of 2.3 volts per cell for 8 hours, the charging 
current being 12.5 amperes. The cells are then arranged in two groups of 
25 cells in series in each group, with the two groups connected in parallel, 
and joined to twenty 50-volt, 50-watt incandescent lamps in parallel, 
(a) Assuming the cells to have an ampere-hour efficiency of 90 per cent, 
for how long a time will the battery light the lamps? (6) What is the 
watt-hour efficiency of the battery if the cells discharge at an average of 
2 volts each? 



By ^ 94 ampere-hours = amperes x hours. 
Ampere-hours input = 12.5 x 8 = 100 an 



X 8 = 100 ampere-hours. 



Each group of 25 cells in series has a capacity of 100 ampere-hours, as 
the capacity of a battery is not increased by connecting cells in series; 



STORAGE BATTERIES 179 

but the capacity of the 2 groups in parallel will be 100 X 2 = 200 ampere- 
hours. Since the ampere-hour efficiency of the battery is 90 per cent, 
the available capacity for lighting the lamps is 200 x 0.90 = 180 ampere- 
hours. The current required for each lamp isl=— = — =1 ampere, 
and the total current for 20 lamps is 20 amperes. 

„, . , ampere-hours 180 „ , , . 

Therefore, hours = = = 9 hours (a). 

amperes 20 

The input in ampere-hours is 100, and the cells charge at 2.3 volts each; 
therefore watt-hours on charge = 100 X 2.3 = 230 watt-hours. Ampere- 
hours out-put from the two parallel groups of cells = 180, whence the out- 

180 
put is = 90 ampere-hours from each group. Cells discharge at 2 volts, 

therefore watt-hours on discharge = 90 X 2 = 180 watt-hours. Then since 

, , , ^ . energy output watt-hours on discharge 

watt-nour efficiency = — — : — ^-— = ^, 

energy input watt-hours on charge 

it follows that 

180 
watt-hour efficiency = — - = 78 per cent (J)). 

163. Methods of Charging. — The voltage required to 
charge a battery must be greater than the discharge voltage 
of the battery. Its value is found by multiplying the number 
of cells in a lead-acid battery by 2.5, and by multiplying the 
number of cells in an Edison battery by 1.75. The charging 
current is controlled so that the charge will take place at an 
appropriate rate, say between the 4-hour and 50-hour rate. 
Some manufacturers designate two charging rates, called the 
''starting'^ and the ''finishing" rates; the latter is used to 
complete the charge after the cells start to gas freely. The 
charging current must always be sent through the battery from 
the positive to the negative pole, in other words, in the direction 
opposite to that in which the current flows through the battery 
during discharge. The positive pole of storage batteries is 
usually marked by a plus sign or the letters POS stamped on 
that terminal, or is painted red, and this terminal must be 
connected to the positive pole of the source of current supply. 
The polarity of the supply mains may be determined by means 
of a polarity indicator, by a voltmeter, or by dipping two wires 
from the supply mains in some water towhich a little salt has 



180 



LESSONS IN PRACTICAL ELECTRICITY 



been added — the terminal from which the least gas (oxygen) 
is liberated is the positive terminal. A direct current only 
can be used for charging storage batteries. Where alternating 
current is the only available source of electricity, it must first 
be converted to direct current by means of a motor-generator, 
a converter, or a mercury- vapor or tungar rectifier. (See Ij 367.) 
For charging portable batteries from a direct-current incan- 
descent hghting circuit where the voltage is greater than that 
of the battery it is necessary to insert a variable resistance in 




i 



Rheostat 



^^ 



A- Charqinqfrom 
110 Volt Circuit 



B-Charging from 
220 Volt Circuit 



^i|'|l|l 

C-Charging 
through Rheostat 



Fig. 122 — Connections for Charging Small Storage Batteries. 



series with the battery and the charging source in order to 
regulate or adjust the charging current to a suitable value. 
This resistance is usually in the form of lamps or a rheostat. 
Fig. 122 A shows the connections for charging a storage battery 
from a 110- volt circuit, using lamps as resistance; the lamps 
are connected in parallel and the entire group is placed in 
series with the battery to- the source of supply; an ammeter 
may be connected in series with the battery to indicate the 
value of the charging current. Where a bank of lamps is used, 
the lamps should preferably be of the carbon-filament type, 
for this type has a greater current consumption for a given 
amount of light than the modern tungsten-filament lamp and 
fewer lamps will be required to obtain any given current. 
Using 110-volt carbon-filament lamps, each 16-C.P. lamp will 
take 0.5 ampere and the 32-C.P. lamp 1 ampere; therefore, 
a bank of lamps having ten 16-C.P. lamps in parallel would 



STORAGE BATTERIES 181 

allow a current of approximately 5 amperes to flow through a 
battery from a 110-volt circuit; five 32-C.P. lamps in parallel 
would also take 5 amperes. In charging from a 220-volt 
circuit, using a lamp bank with 110-volt lamps (Fig. 122 B), 
there would need to be ten parallel groups of two 16-C.P. 
lamps in series in each group, or five parallel groups of two 
32-C.P. lamps in series in each group. To charge from a 
550-volt circuit there would have to be 5 lamps in series in 
each parallel group. When a rheostat is used instead of lamps, 
its resistance should be such as to produce, when carrying the 
proper charging current, a drop in volts equal to the difference 
between the pressure of the charging source and that of the 
battery to be charged (Fig. 122 C). 

Problem 86. — How much resistance would be necessary to insert in a 
rheostat connected in series with a 10-cell lead battery to be charged from 
a 110-volt circuit, if the charging current is to be 5 amperes and the voltage 
across each cell is to be 2.2 volts at the beginning of charge? 

Charging voltage = 10 x 2.2 = 22 volts. Then the voltage across the 
rheostat is 110 - 22 = 88 volts. 

By Formula (29) R = - = — = 17.6 ohms. 
I 5 

Problem 87. — In Problem 86, if a lamp bank resistance were used 
instead of the rheostat, how many 210-ohm (hot resistance) lamps in 
parallel would be needed to make up the desired resistance? 

From Problem 86, the necessary resistance was found to be 17.6 ohms. 

By Formula (31) nq = — = -?12 = 12 lamps. 
J.R. 17.6 

A departure from the foregoing method of charging is advo- 
cated by some users of -lead-acid vehicle batteries, and requires 
the battery to be connected without resistance directly across 
a source of potential whose value is equal to 2.3 times the 
number of lead cells. This method involves no energy losses 
in series resistances and the batteries are charged in a short 
time with very little attention and without overheating and 
gassing. For example, a discharged Type MV "Hycap- 
Exide" 13-plate cell, whose starting and finishing rates are 
specified as 30 and 12 amperes respectively, will take the 
following charging currents at various times after 2.3 volts are 
applied to its terminals: 



182 LESSONS IN PRACTICAL ELECTRICITY 



Time of charge in hours 


Charging current in amperes 





160 


1 

4 


110 


1 
2 


80 


1 


55 


2 


28 


4 


10 



The battery will then be about f charged and ready for almost 
a full day's service. It is advised to give the battery an over- 
charge once a week by raising the potential after the above 
4-hour charging period. If the available source of potential 
has not the proper value, that is 2.3 times the number of cells, 
then a motor-generator will be required to utilize this '^constant- 
potential" charging system, or else use may be made of counter- 
electromotive force cells in series with the battery; these cells 
occasion a constant drop of about 3 volts per cell irrespective 
of the charging current. 

The charging of the storage batteries used in central stations 
and in railway service, which are used at times to carry part 
or all of the station load at the regular line voltage, may be 
accomplished from the line voltage by splitting the battery in 
half and connecting the two halves in parallel, or by using a 
booster to add a sufficient amount to the line voltage to enable 
all the cells to be charged in series. With large batteries 
automatic regulating boosters or end cells with end-cell switches 
are employed in charging. 

164. Uses of Storage Batteries. — The uses to which storage 
batteries may be put are many and varied. They are used 
principally: in central power stations, in isolated plants, for 
telephone and telegraph service, for operating electric motor- 
driven vehicles, and for lighting steam railway cars. They are 
also used on nearly all the modern gasoline automobiles to 
furnish current in connection with a small generator for ignition 
and lighting and for operating the dynamo as a motor to start 
the engine. For this work 6 volts are common, three cells of 
lead-acid battery or five cells of nickel-alkali Edison battery 
being used. A lead starting battery of 100 ampere-hours 
(based on a 5-ampere discharge for lighting) has its starting 



STORAGE BATTERIES 183 

ability expressed bj^ discharging fully at 200 amperes in 10 
minutes. 

Storage batteries are used in central stations in aiding the 
generators to carry the so-called "peaks" of the load which 
may occur regularly at certain periods of the day, such as the 
early morning and evening "rush-hours" of electric traction 
systems, or may happen at any time, such as an unexpected 
load on a lighting central station due to a mid-day storm. The 
battery is charged when the load on the station is light, and 
when an emergency arises, the battery, placed in parallel with 
the generators, assumes its part of the load. This arrangement 
is more economical than the installation of the larger generators, 
prime movers and boilers that would otherwise be necessary 
to carry the peak loads. 

The most important use of storage batteries in central 
station work is to provide an emergency reserve in case of 
accident to the generating machinery, when the battery may 
be called upon to carry the entire load of the station for a short 
time. Many electricity supply companies have large storage 
batteries called "stand-by" batteries for this emergency 
service so as to avoid a stoppage in service. One substation 
of the N. Y. Edison Co. has a battery of 150 lead cells in series 
which is capable of dehvering 12,000 amperes at 240 volts for 
1 hour, or if necessary 50,000 amperes for 6 minutes. Batteries 
are also used for maintaining the voltage constant at the ends 
of feeders or for carrying the entire load during hours of Hght 
load when the generating machinery can be shut down. 

Many of the uses stated above for batteries in central station 
work apply equally well to batteries in isolated plants, such as 
found in some hotels and office buildings. Small isolated 
plants for lighting residences which are remote from a central 
station consist of a 32- or 110-volt storage battery as the 
main supply of current for lighting, a generator driven by a gas 
or gasoline engine being used to charge the battery at convenient 
times, and to supplement the battery when there is a heavy 
demand for current. 

A submarine derives its entire motive power from storage 
batteries when submerged. Such batteries must be of large 
capacity but must occupy a minimum of space and be not too 



184 LESSONS IN PRACTICAL ELECTRICITY 

heavy; in modern submarines the battery constitutes about 
16 per cent of its total weight. 

Batteries for train Ughting furnish current for hghting the 
cars while they are at rest or moving slowly, while a generator 
driven from the car axle furnishes current for the lamps and 
charges the battery when proper speed is attained. 

Batteries used for operating electric motor-driven vehicles 
consist of from 20 to 44 lead cells or 36 to 60 Edison cells; 
to meet the requirements of speed and current for heavy loads 
the battery is connected by a controller through a combination 
of series and parallel connected resistances for furnishing 
current to the motor. 

QUESTIONS 

1. What is the difference between a primary cell and a storage cell? 

2. What does an accumulator store? 

3. What are the active materials of a charged lead-acid storage cell? 

4. Describe the chemical action produced in a lead storage cell by the 
charging current. 

5. Describe the chemical action taking place in a lead cell when it is 
discharging. 

6. What voltage should a fully-charged lead storage cell have? 

7. Why is it not advisable to discharge a storage cell beyond a certain 
point? 

8. How would you determine when a lead storage cell was fully charged, 
and how would you know when to stop the discharge of a cell? 

9. How is the capacity of a storage cell rated, and what is it dependent 
upon? 

10. What are the active materials in the Edison storage cell? Describe 
its action during charge and discharge. 

11. What are the advantages and disadvantages of the Edison storage 
cell over the lead cell? 

12. To what uses are storage batteries put? 

13. How would you charge a 10-volt storage battery from a 110-volt 
direct-current circuit, charging rate to be 5 amperes, extra resistance to 
be made up of incandescent lamps? Make a sketch of connections, 
indicating all polarities, and the number and kind of lamps that you 
would use to obtain the desired current. 

14. A battery is charged for 10 hours, the charging rate being 10 
amperes at a pressure of 25 volts. The battery is then connected to a 
number of lamps requiring for proper illumination a total current of 
5 amperes, (n) If the ampere-hour efficiency is 90 per cent, how long will 
the battery deliver the 5 amperes? (6) What is the watt-hour efficiency 
of the battery if the average pressure on discharge is 19 volts? Ans. (a) 
18 hours; (6) 68.4 per cent. 



LESSON xm 

ELECTROMAGNETISM 

Electromagnetism — Direction of Lines of Force around a Straight Cur- 
rent-carrying Wire — Deflection of a Horizontal Magnetic Needle — 
Right-Hand Rule for Direction of "Magnetic Field around Wires — 
Magnetic Field around a Circular Wire Carrying a Current — Mag- 
netic Field at the Center of a Circular Current — Magnetic Polarity 
of a Circular Current — The Helix and Solenoid — Rules for Deter- 
mining Polarity of a Solenoid — Graphical Field of a Solenoid — 
Questions. 

165. Electromagnetism. — 

Experiment 57. — Connect three or four voltaic cells in parallel, close 
the circuit through a heavy bare copper wire, and then plunge the wire 
into iron filings. The filings are attracted to all sides of the wire, as 
though it were a magnet. Any part of the wire will attract the filings 
when the current is flowing, and the attraction will be equal on all sides of 
the wire, Fig. 123. When the circuit is broken the filings drop from the wire. 

Electromagnetism, as distinguished from magnetism in a 
permanent steel magnet, is the magnetism produced around a 
conductor when a current flows 

through, it. A current of elec- ^,,,,,,^mm^"m^^^^^^^ 

tricity through a wire is respon- ^f^=^=^^^^''^^^^^imimfmm^'^^ 

sible for the magnetic field set 

up around that conductor. The 

fact that every wire carr3dng a ^^^^^-^ 

current possesses this magnetic Fig. 123 -- A Current-carrying 

^ ,, ^, , , 1 • • Wire Attractmg Iron Filmgs. 

field, can be proved by bringmg 

a compass needle near the wire. The magnetic field around the 
wire acts on the compass needle and deflects it. 

Experiment 58. — Pass a heavy copper wire vertically through the 
center of a piece of cardboard held horizontally, upper view of Fig. 124, 
and send a strong current through the wire. Tap the card while sifting 
filings upon it, and they will arrange themselves in concentric circles 
around the wire and at right angles to it. The plan view of Fig. 124 illus- 
trates a graphical field made in this manner. By using paraffin paper the 
picture of the magnetic field may be made permanent by applying heat, 

185 




186 



LESSONS IN PRACTICAL ELECTRICITY 



The filings are magnetic bodies free to move, and arrange 
themselves in the circular direction of the magnetic lines of 

force surrounding the wire. A com- 
pass needle held near the wire will 
take up a position tangent to the 
circular field at any point, whether 
the current be passed up or down the 
wire. The magnetic field, around a 
straight wire carrying a current, con- 
sists of a cylindrical whirl of circular 
lines, as illustrated in Fig. 125, their 
density decreasing as the distance 
from the wire increases. The cir- 
cular lines of force, or magnetic 
ivhirls, do not merge into, cross, nor 
cut each other, but complete their 
circuits independently around the 
wire. 








166. Direction of the Lines of 
Fig. 124. — Graphical Mag- Force around a Straight Current- 
netic Field of a Current- carrying Wire. — 
carrying Wire. 

Made by iron filings. Experiment 59. — Pass a wire vertically 

through a sheet of cardboard held hori- 
zontally. Arrange a number of poised needles or compasses around the 
wire in the form of a circle, Fig. 126, of such diameter that all the needles 
point nearly north and, south. Pass a strong current through the wire, and 
note the result. 

When the "current flows through the vertical wire. Fig. 126, 
the needles, being magnetic bodies, arrange themselves around 
it in the direction 

of the circular M\ /M /@\ /@\ /@\ /M 

lines of force. " *" '^^'^^^^'^''^^^^^^^^^^^^^^'^^S'^'mJ * 
The N-poles of "^ \^ \J \J \J \d/ 

the needles point -^^S- 125. — Magnetic Whirls of a Current-carrying 
in the same direc- 
tion as the magnetic lines of the current, and these lines pass 
through each of the needles, entering at the S~pole and emanat- 
ing at the N-pole, 



ELECTROMAGNETISM 



187 



I 



— b 



If the "N-poles of compasses placed around a vertical wire 
point anti-clockwise, Fig. 126, as you look down upon them the 
current is flow%7ig toward you; if 
the 1^-poles point clockwise, Fig. 
127, the current is flowing from 
you, or, in the same direction in 
which you are looking. 

Experiment 60. — Figs. 126 and 127 
show views of the position of the needles 
on a horizontal piece of cardboard, vvith 
a vertical wire passed through it, when 
the current flows in either direction. 
Using a single compass needle, verify 
the diagrams and make sketches. 



t^^l 



The fact that the needles take 
up a definite direction around 



Fig. 



126.— Current Flowing Up- 
Whirls Anti-clockwise. 



The compass needles on the horizontal 
cardboard arrange themselves in the 
direction of the current's field. 






the wire, is another reason for 
assuming that a current has di- 
rection.' The direction of current in any vertical wire can thus 
be determined with a single magnetic needle, by noting the 

general direction that its N-pole 
C ^j points when presented to the 

|!+ I i . wire. 

167. Deflection of a Horizontal 
Magnetic Needle. — When a 
wire is held horizontally over a 
poised magnetic needle, pointing 
north and south (in the" magnetic 
meridian), Fig. 128, and a cur- 
rent passed through it, the needle 
is deflected and tends to take up 
a position at right angles to the 
wire. When the current is suffi- 
ciently strong, the needle moves, so that it will accommodate 
through itself the greatest number of magnetic Hues of the 
circular field. Considering Fig. 128, the current flows over 
the needle from right to left. As you look along the wire in 
the direction of the current the direction of the whirls is right- 
handed or clockwise, as indicated by the small circles around 



z^ 



Fig. 127. 
Down — 



— Current FlowiQg 
Whirls clockwise. 



188 



LESSONS IN PRACTICAL ELECTRICITY 



the wire; the N-p6le of the needle Ni moves to the position 
N2, at right angles to the wire, and in the direction of the 
field underneath the wire (which is from S2 to N2), so that the 
direction of the whirls and the natural lines within the needle 
are coincident. 

Fig. 129 shows a horizontal wire carrying a current placed over 
or under a magnetic needle in the magnetic meridian and illus- 
trates the direction of deflection of that needle when a current 
flows in either direction through the wire. Since the direction 



Battery 




Fig. 128. 



Deflection of Magnetic Needle under a Hori- 
zontal Wire Carrying a Current. 



of the circular field above the wire is opposite to its direction 
underneath the wire the needle at B will point in the opposite 
direction to the needle at A. Now consider the battery ter- 
minals reversed so that the current flows from left to right 
as at C; the direction of the circular field is reversed and the 
needle under the wire will point in the opposite direction from 
that at A. 

When a current flows from left to right in a wire placed in 
the magnetic meridian under a compass needle and in addition 
from right to left in a wire located over that needle, then the 
needle is deflected to an increased extent in the direction illus- 
trated at E in Fig. 129. (Compare A and D with E of Fig. 
129.) This forms a single turn, or convolution, and increasing 
the number of convolutions increases the extent of the needle's 
deflection till it assumes a position at right angles to the wire 
when the current is sufficiently strong. With the current 



ELECTROMAGNETISM 189 

reversed in the above condition, the needle is deflected in the 
opposite direction. (Compare B and C with F, Fig. 129.) 




-^^s^ -jm 



£ F 

Fig. 129. — Resultant Deflections of the Magnetic Needle when 
Placed near to a Current-carrying Wire. 

The dotted arrows show the position of the magnetic needle before current flows in 

the wires. 

The current flowing in opposite directions, above and below the 
needle, increases the amount of deflection. Equal currents 
flowing above and below the needle, in 
the same direction, produce no deflection, 
(G, Fig. 129.) If two unequal currents 
flow, one above and the other below the 
needle, the needle obeys the directive 
force of the stronger current. 

Experiment 61. — A simple form of apparatus 
for studying the relation between a needle's 
deflection and the direction of current, called an 
Oersted stand, is shown in Fig. 130. It consists 
of two parallel brass rods provided with binding 
posts and supported from a wooden base. With 
it the student should verify all the cases given in Fig. 129 and make sketches. 

168. Right-Hand Rule for Direction of Magnetic Field 
around Wires. — If the direction of the current in a straight 
wire is known then the direction of the circular magnetic field 
around that wire can be determined, or vice versa. The rule 
follows : 




Fig. 130. — Oersted 
Stand for Studying the 
Needle's Deflection by 
a Current. 



190 



LESSONS IN PRACTICAL ELECTRICITY 



Magnetic Lines 




Grasp the wire with the fingers of the right hand and allow the 
thumb to he extended in the direction of the wire as shown in Fig. 

ISl; if the thumb points in the direc- 
tion of the current then the] fingers 
indicate the direction of the lines of 
force around the wire. 

169. Magnetic Field around a 
Circular Wire Carrying a Cur- 
rent. — 

WcfhtHand Experiment 62. — Mount a circular 

T?- 101 T)-i,+ u j-Di' turn of wire vertically in a piece of card- 

f ^^" \- T.- T ,n ? board, so that one-half of the circle will 

tor t mdine Direction oi Current , , ' - u i • .. i i • -i^- 

or Direction of Magnetic Whirls, ^l^^^'l^ *^^ horizontal plane as in Fig. 

132. Pass a current through the wire, 
and, while tapping the cardboard, sift iron filings over it. 

The iron filings will be found to arrange themselves circu- 
larly around the wire. Near the center of the loop the fiHngs 
are nearly parallel with its axis. If the field around the loop 
be explored with a com- 
pass needle it will always 
lie in the direction of the 
fiHngs at the point chosen 
and its N-pole points in 
the direction of the field. 
The arrows in Fig. 132 in- 
dicate the direction of the 
whirls. 

Apply the right-hand 
test (H 168), and it will ^ig- 132 
confirm the position the 
needles take up at any 
point. On one side of the loop all the whirls enter it in the 
same direction, and they emerge from the opposite side, as is 
further shown in Fig. 133. 

170. Magnetic Field at the Center of a Circular Current. — 
If a magnetic body, such as A, Fig. 133, be held above a circular 
loop through which a current is flowing, it will tend to move 
downward through the loop, with its axis coinciding with the 
axis of the loop, until its position accommodates through itself 




Graphical Field of a Circular 
Current 

Made with the aid of iron filings. 



ELECTROMAGNETISM 



191 




Fig. 133. — Attraction of Magnetic 
Body A by the Magnetic Field Due to a 
Current Flowing in a Circular Loop of 
Wire. 



the greatest number of lines of force of the field (If 20). There 
will be the same tendency in B, Fig. 134, where the current is 
flowing in a long rectangular 
circuit; but it will be seen 
from inspection of the two 
figures that many more of 
the lines of force due to the 
current act upon the mag- 
netic body when the circuit 
is in [the form of a circular 
loop than when in a rectan- 
gular or any other form. 
The smaller the radius of a 
circular loop the greater will 
be the strength of the field 
at the center of that loop for the same current in the wire. 
Doubling the current will double the field strength. 

171. Magnetic Polarity of a Circular Current. — Under the 
subject of Magnetism, we assumed the magnetic lines of force 
to pass out from the N-pole of a bar magnet and enter the 
magnet again at its S-pole; a similar reasoning is applied to 
the magnetic lines of force of an electric circuit. In the single 

turn of wire, Fig. 133, the 

current flows around the 

loop in the direction of 

the hands of a watch. The 

circular whirls 'are also 

clockwise, if you look along 

the wire in the direction of 

Fig. 134. — Attraction of Magnetic the current. The magnetic 

Body B by the Field Due to a Current ^^1,1^1^ therefore, all enter 

Flowing in two Parallel Wires. , . ' , , ' . , 

the loop through its upper 

side, or face; consequently, this face possesses S-polarity, and as 
the same lines emanate again from the under face, that face is 
of N-polarity. The single turn of wire, therefore, possesses 
polarity similar to ^a bar magnet, and when free to move will 
take up a position in the earth's field with its N-face pointing 
toward the north; also, its N-face will be repelled by the N-pole 
of a similar loop or bar magnet, and attracted by the magnet's 




192 



LESSONS IN PRACTICAL ELECTRICITY 




S-pole, according to the law of attraction and repulsion between 
magnets. 

172. The Helix and Solenoid. — A coil of wire wound so 
as to follow the outlines of a screw without overlaying itself 

is termed a helix (Fig. 135) and 
may be wound right- or left- 
handed. If the current enters at 
the right-hand wire of Fig. 135 
the magnetic field will be directed 
toward the 
left, as shown. 
Fig. 135. — Direction of the Field This polarity 
of a Hehx. f -^ 

can be re- 
versed by rewinding the helix in the oppo 
site direction, or by simply sending the 
current through the helix in the opposite 
direction. A solenoid is a coil of wire, gener- 
ally wound on a wooden or other insulating 
spool, the length of which is usually greater • 
than the diameter, Fig. 136. The winding 
is always in the same direction, layer upon 

layer, similar to the winding of a spool oi ^. ^^^ 

xi 1 rm, -1 r 1,1- 1 -1 Fig. 136. — Solenoid. 

thread. The spirals ot a helix or solenoid 

are equivalent in their magnetic action to as many circular 





Fig. 137. — Polarity of a Helix or Solenoid. 

The whirls of one turn unite with those of the next. 

currents as there are convolutions of wire, since their axes lie 
in the same straight line. The magnetic whirls of each turn 



ELECTROMAGNETISM 



193 




Fig. 138. — Poised Solenoid. 

The movable coil is poised on needle 
points. 



inside the helix are in the same direction as of every other 
turn, and the direction of the magnetic field along and parallel 
to the axis of the solenoid is straight 
and fairly uniform to within a short 
distance of the ends. The total 
field within the solenoid is made 
up of the magnetic lines of the in- 
dividual turns, as illustrated in the 
heHx of Fig. 137, where the whirls 
of each convolution are depicted; 
the sum of the whirls of all the 
turns constituting the total field, 
or number of lines of force passing 
through the helix. This diagram 
shows the direction of current 
through the helix, the direction of 
the whirls around each convolution, and the resulting polarity 
of the hehx. The action is similar for another set of convolu- 
tions wound'over this set in the same direction, or for a sole- 
noid composed of any number of layers of winding. The 

strength of the magnetic field 
of a solenoid depends upon 
its number of turns and the 
amount of current flowing in 

Direction of y,^ ITlf^ W ¥ Wll W \\ them. 

Magnetic Force ^ „ „ ^ 

"" ' ' "" ' ' ' Experiment 63 — Testing the 

Polarity of a Solenoid. — When a 
current is passed through a sole- 
noid it behaves similar to a mag- 
net. A suspended, or poised sole- 
noid, Fig. 138, is convenient for 
testing the polarity. The two 
terminals of such a solenoid dip into two concentric circular grooves con- 
taining mercury by which contact is made. One groove is connected 
to each binding post by a wire, the groove stamped A corresponding with 
post A, so that the direction of the current may be traced. When a cur- 
rent is sent through the movable coil it takes up a position N-S, just as in 
the case of the poised needle; it is also repelled or attracted by another 
magnet or solenoid. 

173. Rules for Determining Polarity of a Solenoid. — Clasp 
the solenoid, or helix, in the right hand so that the fingers point 




Fig. 



"^/'rection^ of Co^ 



139. — - Right-hand Rule for the 
Polarity of a Solenoid. 



194 



LESSONS IN PRACTICAL ELECTRICITY 





Fig. 140. — Clock Rule for 
Polarity. 



around it in the direction that the current flows. The out- 
stretched thumb, at right angles with the fingers, will point 
to the N-pole of the solenoid, Fig. 139. 
To find the direction of current around the coil when the 

polarity is known: clasp the coil 
with the right hand, so that the 
thumb outstretched at right angles 
will point toward the N-pole, then 
the fingers will point in the direc- 
tion of the current. 

If, on viewing the end of a sole- 
noid, the current flows around that 
end in the same direction that the hands of a watch move. 
Fig. 140, then that end is of S-polarity. If the current flows 
around the coil against the direction in which the hands of a 
watch move, that end possesses N-polarity. 

174. Graphical Field of a Solenoid. — The distribution of 
magnetism around a solenoid is very 
similar to that of a bar magnet, and 
can be studied by the iron fifing dia- 
gram, Fig. 141. 

Bxperiment 64. — Cut a piece of card- 
board to fit around a solenoid, as in Fig. 
141. Place the cardboard horizontally so 
that its plane is in the axis of the coil. Pass 
a current through the coil, and, while gently 
tapping the cardboard, sift iron filings on it 
to produce a graphical field. I 

Experiment 65. — Wind a helix about 1 
inch in diameter and 4 inches long. Cut a 
tongue in a sheet of cardboard equal to the 
inside 'diameter of the helix, and pass it 
horizontally through the helix with its plane 
in the axis of the helix. Make a graphical 
internal field of the helix. The direction of 
the lines of force may also be explored by a compass needle. 




Fig. 141. — Magnetic Field 
of a Solenoid. 

Illustrated by iron filings upon a 
horizontal piece of cardboard. 



QUESTIONS 

1. A feeder for an overhead trolley line is conducted up a vertical 
wooden pole from an underground duct. When you approach the pole 
from the south, the N-end of a compass needle held in your hand is de- 
flected east. Is the current flowing up or down the pole? 



ELECTROMAGNETISM 195 

2. One end of a solenoid attracts the N-pole of a compass needle. What 
is the direction of the current around the coil when viewed from this end? 
.3. Two parallel lines, one above the other, are stretched in a north- 
south direction, and equal currents flow through them in the same direc- 
tion. A compass is held midway between the wires. How will its needle 
be affected? Make a sketch. 

4. Six successive turns are made in a right-hand direction around a 
lead pencil, and the following six successive turns are wound in the oppo- 
site direction. A current is passed through the wire. Sketch the direc- 
tion of the magnetic field you would expect to see if iron filings were used, 
and indicate the polarity and direction of the current. 

5. A current is sent through a coil of wire wrapped around a tumbler 
in the same dkection that the fingers of the right hand point when clasp- 
ing it to drink. What is the polarity of that end of the coil you observe 
while drinking? 

6. A current is passed through a wire held east and west over a com- 
pass needle. How will the needle be affected? Make a sketch. 

7. You are given the terminals of a cable connecting with the positive 
and negative poles of 5 voltaic cells. The terminals are to be connected 
so that the cells will all be in series. How would you proceed by the 
use of a galvanometer to determine the polarity and make the connections? 
Give sketch. 

8. The N-pole of a bar magnet, lying on a table with its axis pointing 
east and west, deflects the N-pole of a compass needle 20 degrees. A wire 
carrying a current is held over the compass in a north-south direction 
and the deflection is now only 12 degrees. How do you account for this? 
What is the direction of the current through the wire? Make sketch. 

9. An electric-light wire is run up the south wall of a building from the 
first to the second story. Walking toward the wire the N-pole of a com- 
pass held in your hand is deflected east. What is the direction of the 
current in the wire? Make a sketch. 



LESSON XIV 

ELECTROMAGNETS 

Magnetization of Iron and Steel by an Electric Current — Magnetic 
Field of an Electromagnet — Attractive Force of a Solenoid for an 
Iron Core — Circuit Breakers — Magnetic Circuits — Typical Forms 
of Electromagnets, their Construction and Use — Polarized Electro- 
magnets — Magnetomotive Force — Field Intensity — Law of the 
Magnetic Circuit — Magnetic Density, Permeability and Reluctance 
— Table X — Calculation of Magnetic Circuits — Magnetization 
Curve — Attractive Force of an Electromagnet — ■ Questions and 
Problems. 

175. Magnetization of Iron and Steel by an Electric 
Current. — 

Experiment 66. — Wind a number of turns of insulated wire around an 
iron bar, Fig. 142, and send a current through the wire. Plunge the bar 

into iron filings, and it is found to attract 
li them mostly at the ends, and when the cur- 

rent is interrupted the filings drop off. Test 



-I 



N f iJ 7 ] J 7 J 7 „) S tne polarity of each end of the bar with a 

VA compass. Note that upon looking at the end 




|. of the bar which repels the N-pole of the com- 

_____ ^"\* pass the current flows around the winding in 

Qf\ ~\ \ "\ "^ ^ -A N the opposite direction to that in which the 
,;,^j;,„.J..,|,i;.J...f>.4////V j^^^^g ^f ^ ^^^^^ ^^^^ (p.g_ J42). When 

'/■*■ xJffTfT^ viewing that end which attracts the N-pole 

of the compass, the current flows around the 
wire in the direction that the hands of a watch 
move. Figs. 142 and 143 illustrate the po- 

Y[a 142 Current Anti- Parities of a steel bar, according to the clock 

clockwise — N-Polarity. I'ule, for all possible changes in either the 
direction of current or the direction of wind- 
ing with a given direction of current. 

Experiment 67. — Remove the bar from the coil and note that the 
polarity of each end of the helix is the same as with the bar inside of it; 
the magnetism was, however, much stronger when the bar was inserted 
in the coil. If suspended or poised (see Fig. 138), the helix and its iron core 
wiU take up a position in the earth's field similar to the compass needle. 
It will also attract or repel the poles of a like helix and core according to 
the law of attraction and repulsion. 

196 



ELECTROMAGNETS 197 

When a piece of hard steel is placed in the vicinity of an 
electromagnetic field, many of the lines of force of the field 
are bent out of their natural direction and converge into the 
steel. There are now more lines of force passing through the 
space occupied by the steel than when this space was occu- 
pied by air alone. The capability of any substance for conduct- 
ing magnetic lines of force is termed its permeability; therefore, 
the permeability of the steel is much greater than that of air. 
When a piece of soft iron is substituted for the steel, even 
more lines of force will pass through the same space, showing 
that the permeability or conducting 
power of iron is greater than that of 
steel. The permeability of iron may 
be" several thousand times that of air, 
that is, several thousand times as 
many lines of force will pass through 
space when occupied by iron as when 
it is occupied by air. An iron bar in- 
serted in a helix or solenoid is a much 
better conductor of the magnetic whirls 
inside the solenoid than the air, so that 
the strength or attractive force of the ^'^- 11^; ~ c pXl?^'^" 

. .,-,. -,-, 1 wise — D--r oiarixy. 

solenoid is materially increased, though 

the magnetizing current is the same as before. An iron core 
introduced into a solenoid carrying a current becomes strongly 
magnetized. 

The solenoid with its core is called an electromagnet. The 
direction of the lines of force through the iron core of the sole- 
noid is the same as their natural direction through the solenoid 
alone, so that all the laws for polarity of the solenoid given 
under Electromagnetism, Lesson XIII, apply also to an elec- 
tromagnet. By applying the molecular theory of magnetism, 
K 13, the phenomenon of magnetism in the iron bar pro- 
duced by the magnetic effect of the current will be understood. 
The magnetic field due to the current in the wire acts induc- 
tively upon the molecules of the iron bar, causing them to 
change the relation of their internal magnetic circuits with 
respect to each other, thus producing an external field very 
much in the same way that a permanent magnet acts on them^ 




198 



LESSONS IN PRACTICAL ELECTRICITY 



The current's magnetic field simply makes evident the latent 
magnetism of the iron. This molecular action also accounts 
for the permanent magnetism produced in a piece of steel 
within a solenoid after the current ceases, since the internal 
molecular friction prevents many of the molecules from resum- 
ing their original positions. 

176. Magnetic Field of an Electromagnet. — The picture 
of the magnetic field of a solenoid and core, or straight bar 

electromagnet, produced by iron 
filings would be similar to that of a 
solenoid alone, as in Fig. 141, except 
that the fihngs would be attracted 
more closely together, illustrating 
the greater density or number of 
lines of force due to the iron core. 
A compass needle, used to explore 
the field, will take up the same posi- 
tion as with the solenoid alone, but 
it is now affected at a much greater 
distance. The magnetic lines of 
force emanate from the N-pole of 
the bar electromagnet, and complet- 
ing their path through the external 
medium enter the magnet again at 
its S-pole. If the iron core of the solenoid be pulled out some- 
what from the coil, and filings be again applied, the magnetic 
lines will be found to be conducted further away from the coil 
before returning to it, as in Fig. 144. The polarity is still the 
same as before, but the poles are not so strong as when the 
whole internal field of the solenoid was composed of iron. 

177. Attractive Force of a Solenoid for an Iron Core. — 
When under the attractive influence of a solenoid, an iron 
bar is subjected to a pull, the magnitude of which depends 
upon the relative position of the two bodies and the magnetiz- 
ing current. If either body is free to move, and the force 
sufficiently strong, the body will move to accommodate through 
the core the greatest possible number of lines of force. This 
attractive force may be measured by attaching the bar to a 
spring balance, as shown in Fig. 145. While balanced, test 




Fig. 144. — Magnetic Field of 
a Solenoid and Core. 

Shown with iron filings on a hori- 
zontal piece of cardboard. 



ELECTROMAGNETS 



199 



. spring 
BalancQ 




the polarity of the bar by a compass; it is magnetized by in- 
duction (H 21) with the polarities as shown. Note that a 
number of the magnetic lines from the solenoid complete their 
circuit through the core, entering at its upper end, which is 
consequently of S-polarity, and emanating 
from the lower or N-end to pass through 
the coil. Place the solenoid nearer to the 
core, or lower the core to it, and the pull 
will be considerably increased. The term 
"sucking coil" is sometimes applied to the 
solenoid when used in this way with its 
core. This principle is extensively applied 
to operate the feeding mechanism in arc 
lamps, to automatically open switches in 
electric circuits when the current becomes 
excessive, as in the circuit breaker, If 178, 
to close switches at a distance for remote- 
control purposes, and to actuate commercial 
instruments for measuring current and pres- 
sure, Lesson XVII. 

178. Circuit Breakers. — A circuit breaker 
is primarily designed to protect electrical circuits against ab- 
normal conditions arising therein. The most usual form of 
circuit breakers is the plain overload type 
which, as its name suggests, opens the cir- 
cuit in the event of overload, or excessive 
current. As the circuit breaker is usually 
made, its response to overload is almost in- 
stantaneous, but by the addition of a simply- 
constructed 'Hime-Kmit" device, the action 
may be delayed so that the circuit is opened 
only after the overload has been carried for 
a brief period, this period automatically 
becoming less as the overload becomes 
greater. 

Circuit breakers may also be equipped with a '' no-voltage " 
device for opening the circuit when the voltage falls to a pre- 
determined point; with a ''shunt-trip" feature, for opening 
the circuit from push buttons placed at conveniently located 



Fig. 145. — Measur- 
ing the Magnetic At- 
traction of a Solenoid 
for its Iron Core. 




Fig. 146. — ■ Circuit 
Breaker. 



200 



LESSONS IN PRACTICAL ELECTRICITY 



points; with a ''reverse-current" arrangment, which opens the 
breaker upon reversal of the direction of current flow (thus 
affording a form of protection which is desirable where genera- 
tors arje operated in multiple and also for circuits from which 
storage batteries are charged); and with a ''reversal of phase" 
feature for polyphase alternating-current circuits for protec- 
tion against reversal of rotation of motors. In addition to the 
various protective features mentioned above, any of these cir- 
cuit breakers may be equipped for closing as well as for open- 
ing the circuit from a remote point. This is accomplished 
by closing mechanisms operated by a motor, a solenoid, or 
compressed air. 

179. Magnetic Circuits. — A simple magnetic circuit of 
uniform cross-section is represented by the solid iron ring 




Fig. 147. — The Magnetic Polarity of an Iron Ring. 

in A, Fig. 147, around which a number of turns of insulated 
wire have been wound. The direction of the current and the 
resulting polarity of the coil are shown, while the arrows indi- 
cate the direction of the lines of force around the ring. If a 
ring, so magnetized, be plunged into iron filings it will not 
show any external poles, since the magnetic lines have a com- 
plete circuit through the iron. 

When a small air-gap is made by sawing out a small section 
of the ring (B, Fig. 147), the lines of force are compelled to pass 
through the air gap to complete their circuit, so that strong 
N- and S-poles are produced where the cut has been made, and 
the space is permeated with lines of force. The lines of force 
through the iron circuit are not nearly so dense as before, since 
the "resistance" of the circuit has been increased. With the 
same magnetizing force the magnetic lines diminish as the 



ELECTROMAGNETS 



201 



resistance " of the circuit increases, just as in an electric circuit 
the current decreases when, with a constant pressure, the re- 
sistance is increased. If the removed section of the ring is now 
replaced and the ring again plunged into iron filings while the 
core is magnetized, a great many filings will be attracted at 
the two joints, thus illustrating magnetic leakage. The flux 
density in the ring is not now so great as when it was solid, 
since the joints offer opposition to the magnetic lines and some 
of them are forced through the air across the joint. 

A solid ring with two poles is shown in C, Fig. 147, the 
winding being in the same direction throughout the ring, and 
the ends of the wire being joined together. Current is sent 
in at any point and flows around both halves of the ring in 
opposite directions to a diametrically opposite point and then 
back to the battery. The arrows indicate the direction of 
current and magnetic lines of force, and it will be seen that 
a consequent N-pole is produced at the top of the ring and 
a S-pole at the bottom. The lines of force complete their path 
through the air from pole to pole, as will be noted by plunging 
the ring into iron filings. 

Experiment 68. — Connect a horseshoe electromagnet with a source of 
current so that the Hnibs are hke poles. Attract the keeper and then 
plunge the magnet into iron filings. One pole is produced in the center 
of the keeper and the opposite pole in the bend of the horseshoe. The 
magnetic distribution is similar to that of the solid ring with two poles in 
C, Fig. 147. 



..■■Iron Con 



180. Typical Forms of Electromagnets, their Construction 
and Use. — If the bar 

electromagnet, Fig. 142, 
is bent around into a U 
shape, as in Fig. 148, 
it forms a horseshoe 
electromagnet, thereby 
increasing the attrac- 
tive power. Instead of 
winding the insulated 
core directly upon the 
wire, as shown at the 




Fig. 148. 



Horseshoe Electromagnets with 
Keepers. 



left, it is generally wound upon wooden or brass bobbins 



202 



LESSONS IN PRACTICAL ELECTRICITY 



several layers deep, which are then slipped over the soft iron 
horseshoe core, as in the right-hand view of Fig. 148. The 
two spools are then connected by wires so that the current 
will flow around the spools in the opposite directions, as viewed 

from the end of the core, in order 
that the limbs will have opposite 
polarity. The attractive force of 
the magnet may be tested by 
means of a keeper of adequate 
cross-sectional area, provided with 
a handle or hook. 

Instead of a forged horseshoe 
the practical horseshoe electro- 




Fig. 149. — Polarity of 
Horseshoe Magnet for a Given magnet is usually made of three 
Direction of Current. ^^^^^^ ^^ .^ j..^^ ^49^ ^^^^^ ^^^ 

two iron cores or limbs are connected by an iron yoke of 
equivalent cross section and secured by machine screws. The 
direction of current and resulting polarity of the cores are 
also illustrated. 

Horseshoe electromagnets are used in many practical appli- 
cations of electricity, as in 
electric bells, automatic gas- 
lighting burners, telegraph 
sounders and relays, etc., 
and are designed and con- 
structed to best perform 
the required service. The 
sounder. Fig. 150, of the 
telegraph consists of a 
horseshoe electromagnet 
which attracts a small soft- 
iron armature when a cur- 
rent is sent through the coils, and when the current is turned 
off the armature is released and pulled away from the cores 
by a spring. The clicks produced on attraction and release 
are interpreted in accordance with a telegraph code. 

A form of electromagnet that will produce a very powerful 
attraction at a short distance is constructed of a short cylin- 
drical soft iron core with the proper winding upon it and sur- 




Fig. 150. — Telegraph Sounder. 



ELECTROMAGNETS 



203 




Fig. 151. — Ironclad 
Electromagnet. 



rounded by an outer iron tube, the iron tube and core being 
united at one end by an iron yoke, Fig. 151; the iron jacket 
forms a return path for the lines of force 
and the poles are concentric. This type, 
known as an 2Vo?2cZac^-electromagnet, is em- 
ployed where a strong attraction is desired 
when the armature, or object it is to hold, 
is in actual contact with the polar surfaces. 
If the armature is removed a small distance 
from the concentric pole's, there will be con- 
siderable leakage of magnetic flux between 
the core and outer iron jacket; therefore its 

use is limited to cases 
where the attracting 
distance is small. 
Small electromagnets 
of this type are used 
in telephone switch- 
board apparatus 
where the range of 
action is not great and 
the exciting current is 
of short duration. 

Large ironclad elec- 
tromagnets are made 
from a solid piece of 
iron or steel casting, 
having a groove turned 
in the casting to re- 
ceive the exciting coil. 
This type is well 
adapted for lifting pur- 
poses and many are 
now in use in large 
industrial plants for 
handling iron and steel 
of all descriptions. 
Fig. 152 shows a large lifting magnet of this type. 

The lifting power of an electromagnet is proportional to the 




Fig. 152. 



Lifting Magnet in Operation. 



204 



LESSONS IN PRACTICAL ELECTRICITY 




Fig. 153.— Horse- 
shoe Magnet with 
Greatest Attraction 
at its N-Pole. 

N-pole is smaller in area 
than the S-pole. 



square of the density of the lines of force per square inch and 
the area of the contact surface. This fact explains a peculiar 
phenomenon relating to lifting magnets. In an ironclad elec- 
tromagnet used for Ufting purposes, the 
greater the area of the polar surfaces and 
the surfaces of material to be lifted, the 
greater will be the attraction; but after 
actual contact the attraction is greater when 
the polar or attracting surfaces are smaller. 
When the area of contact is decreased the 
flux density (number of lines of force per 
unit area) through the smaller contact sur- 
faces is increased by the lines crowding into 
them, and as the attractive force is propor- 
tional to the square of the density, a decrease 
in contact area may cause the square of the density to be in- 
creased more than the area is diminished, thus increasing the 
lifting power. Considering the 
magnet in Fig. 153 when the arma- 
ture is in actual contact with the 
core, the attraction will be greater 
at the N-pole than at the S-pole. 
The most important use of elec- 
tromagnets is in generators and 
motors where they are used to 
create the intense magnetic fields 
necessary for the development of 
large quantities of electric power. 
Fig. 154 represents the field coils 
and the magnetic circuit of a two- 
pole dynamo. 

181. Polarized Electromagnets. 
— A combination of a permanent 
magnet and an electromagnet is called a polarized electromag- 
net. In this type the whole magnetic circuit is normally 
under the influence of the permanent magnet alone, and when 
a current is sent through the electromagnet coils the polarity 
of the cores due to the permanent magnet may be strengthened, 
partly or wholly neutralized, or even reversed. This type is 




Fig. 154. — Field Coils and 
Magnetic Circuit of a Two-pole 
Dynamo. 



ELECTROMAGNETS 



205 




extensively used in telephone ringers, Fig. 155. The magnet 
coils M and M' are formed of a great many turns of fine wire 
wound upon soft iron cores, the cores being attached to the 
iron yoke Y. The soft iron armature n, pivoted at F, has the 
clapper rod C attached to its center so that every movement 
of the armature will cause the ball at the upper end of the 
clapper to strike the bells. 

The permanent magnet N extends from the yoke, back of 
the coils, to a point somewhat below the armature. The arma- 
ture is magnetized inductively by 
this permanent magnet, whose N- 
pole is opposite the center of the 
armature, and a S-pole is induced 
in the armature at that point, 
and the ends of the armature be- 
come N-poles. With no current 
flowing in the coils, either end of 
the armature will attract its adja- 
cent magnet core. When the 
current flows in such direction 
through the electromagnet winding ^, Fig- 155. — Telephone Ringer 
° ,, Ti/r i 1 Using Polarized Type of Electro- 

so as to cause the core M to be- magnet. 

come a N-pole and the core M' a 

S-pole, the right-hand end of the armature will be attracted 
by the S-pole of the electromagnet and the other will be repelled 
by its N-pole, causing the armature to be tilted and moving 
the clapper to the left. On reversing the current, the polarity 
of the magnet cores will be reversed, causing the armature to 
be tilted in the opposite direction. When alternating current is 
used in ringing, the polarity of the magnet cores is reversed 
just as often as the direction of current in the coils is reversed, 
causing the armature to be tilted from one side to the other 
every time the current reverses, the ball of the clapper striking 
one of the gongs each time. 

The polarized relay illustrated in Fig. 156 and commonly 
used in some telegraph circuits consists of a polarized elec- 
tromagnet. The permanent magnet N'S' is of horseshoe 
form, and is also bent in the arc of a circle as viewed from 
above. The two electromagnets are mounted vertically and 



206 



LESSONS IN PRACTICAL ELECTRICITY 



carry pole pieces which face each other. Two armatures, 
mounted on a common shaft, are arranged so that each works 
between a pair of pole pieces of the electromagnet. Each 
armature, being pivoted near one end of the permanent mag- 
net is inductively magnetized ; assuming the end of the magnet 
near which the upper armature is pivoted to be of S-polarity, 
then the armature at that end will have N-polarity, but its 
other end which moves between the upper electromagnet 
pole pieces will be of S-polarity. Similarly, the poles of the 
electromagnets, being under the influence 
of the permanent magnet, are inductively 
magnetized north polarity at the upper 
ends and south at the lower ends, that 
is when they are not neutralized or re- 
versed by current flowing through the 
electromagnet windings. Therefore, with 
no current flowing through the electro- 
magnet, the armatures (having no direc- 
tive springs) when placed midwaj^ between 
the electromagnet poles will be attracted 
equally by them; the field of the per- 
manent magnet tends to hold the arma- 
tures in a balanced position, so that the 
armatures may be moved in either direc- 
tion at will, according to the direction of 
current through the electromagnet. There are two windings on 
the electromagnet, namely 1-3 and 2-4, which may be con- 
nected in series or in parallel as preferred; they are connected 
in series in Fig. 156. When the electromagnet is energized by 
a current entering at terminal 1 the magnetism thus produced 
in its cores increases the N-polarity of the left upper pole and 
weakens the right, it also increases the south polarity of the 
left lower pole and weakens the right; thus both armatures are 
attracted by the strengthened left-hand poles and contact is 
made between the tongue contact 5 and contact screw 6. The 
armature in polarized relays used for unidirectional current 
instead of being balanced is held by means of a spring toward 
one pole of the electromagnet, and a current of proper polarity 
will move the armature to the opposite pole. 




Fig. 156. — Construc- 
tion of Polarized Relay. 



ELECTROMAGNETS 207 

182. Magnetomotive Force. — 

Experiment 69. — Connect the coils of an electromagnet wound with 
many turns of wire in series with another magnet wound with a few turns 
of wire and join them to a battery. Plunge each magnet into iron fihngs. 
The magnet wound with many turns attracts more fihngs yet, since they 
are in series, the current strength is the same through each magnet. The 
magnetism depends upon the number of turns, as well as upon the current. 

Experiment 70. — Note the pull, required to detach a keeper from the 
poles of its magnet when the spool, wound with 400 turns of fine wire, has 
1 ampere passed through it. Now substitute another spool wound with 
40 turns of much larger wire through which 10 amperes are sent. It will 
be observed that the keeper is detached by the same force as before. 

From the above experiments it will be seen that the mag- 
netism, or magnetic fiux (total nmnber of hnes of force), de- 
pends upon the turns as well as upon the current strength; 
the current and number of turns being jointly responsible for 
the force that drives the magnetic fiux around the magnetic 
circuit, just as an electromotive force drives an electric current 
around an electric circuit. The magnetizing force set up by 
a current flowing through a solenoid or any coil of wire is 
called the magnetomotive force (abbreviated m.m.f.); it is 
directly proportional to the current and to the number of 
turns in the solenoid. The magnetomotive force is, therefore, 
proportional to the product of the number of turns and the 
current strength. If the latter be in amperes, the magnetomo- 
tive force may be expressed in a unit called the ampere-turn. 

To FIND THE MAGNETOMOTIVE FORCE OF A COIL IN 
AMPERE-TURNS : 

Multiply the number of turns upon it hy the strength of current 
passing through it. 

For example: four amperes circulating 25 times around a 
coil produce a magnetomotive force of 100 ampere-turns. The 
same force could be produced by 2 amperes and 50 turns, or 
by 100 amperes and 1 turn, etc., the product of the turns and 
current in each case being 100. 

Let I = current in amperes, 

T = number of turns on the coil. 

Then the magnetomotive force is 

ampere-turns = I x T . . . . (68). 



208 LESSONS IN PRACTICAL ELECTRICITY* 

Like results may be accomplished by magnets wound with 
coarse wire or with fine wire; each type has its advantage 
according to the manner in which it is to be used. The mag- 
nets of an electric bell, telephone, or telegraph instrument are 
wound with fine wire, as they are usually located at some dis- 
tance from the battery, so that the current may be very small, 
and the line small in area, the required magnetizing force being 
produced by a small current flowing through a large number 
of turns. When it is desired to operate a small magnet from 
a 110-volt circuit it is wound with fine wire, so that its resis- 
tance will be high and the current requirement small, thus 
making it inexpensive to operate. The same magnetic pull 
could be obtained with a coarse wire magnet in the latter case, 
using a large current, at an increase in the cost of operation. 
Electromagnets operated' in series, as in arc lamps, circuit 
breakers, etc., are wound with coarse wire, having a low resis- 
tance, since the whole current passes through the coil, the mag- 
netizing force being produced by a large current and few turns. 

It is necessary to express the magnetomotive force in terms 
of magnetic units, as follows: It has been found by ex- 
periment that one ampere-turn will produce 1.257 fines of 
force through an air-path one centimeter in length and one 
square centimeter in cross-sectional area; one ampere-turn 
will also produce nearly 3.2 lines of force through an air-path 
one inch long and one square inch in cross-sectional area. 
The total magnetizing force, or magnetomotive force, ex- 
pressed in magnetic lines through a one-inch cube of air equals, 
then, the ampere-turns multiplied by 3.2, or the magnetomo- 
tive force in magnetic units is 

m. m. L = 3.2 X I X T (69). 

Thus, if we had a solenoid wound with 50 turns of wire and a 
current of 2 amperes flowing around them, the magnetic pres- 
sure would equal 3.2 x 2 x 50 = 320 magnetic units. The 
above value of m. m. f. represents the magnetic pressure for 
the total length of the core of the solenoid or coil. 

183. Field Intensity. — In magnetic calculations the mag- 
netomotive force per unit length of the magnetic circuit is of 
great importance, and is called the intensity of the magnetic 



ELECTROMAGNETS 209 

field. This field intensity is the magnetomotive force divided 
by the length (1) of the magnetic path, and is represented by 
the letter X. It was pointed out in ^ 182 that one ampere- 
turn produces 1.257 lines of force through a cube of air one 
centimeter on a side. Therefore, the field intensity is 

^^ m. m. f. 1.257 X I xT ._^. 

'J^ = — j — = j ; Uv;. 

where 1 is the length of the path in centimeters. 

If the length (1) of the magnetic path of a solenoid is known, 
the m. m. f. necessary to produce a desired field intensity (DC), 
is obtained by multiplying 'DC x\. 

For example: suppose we have a coil of 25 turns, the coil 
being bent in a circular shape to form a complete ring. Fig. 
147, so there will be no free poles. Each fine of force would 
have a complete path inside the coil, so that the length 
of the magnetic circuit can easily be measured. A current of 
20 amperes flowing through the coil would give, by Formula 
(68), a magnetizing force in ampere-turns of 500. If the mean 
length of the magnetic circuit is 12.5 centimeters, then the 
magnetomotive force per centimeter length, by Formula (70), 
becomes 

^ "1.257 X I X T 1.257 X 20 x 25 ..^ 
^ = 1 = 12:5 = ^^-^^ 

meaning that a uniform magnetic field is produced in the 
solenoid of 50.2 lines per square centimeter, or 50.2 x 2.54 
X 2.54 = 324 lines of force per square inch of sectional area. 
The above is true only for a solenoid with a core of air or other 
non-magnetic substance. 

The two formulae just given for determining the values of 
'DC and m. m. f. are very similar and the distinction between 
them should be kept clearly in mind. The quantity DC repre- 
sents the force magnetizing a unit length of the core of a 
solenoid, or the strength of field in lines of force per square 
centimeter or per square inch, within a coil with an air core. 
The quantity m. m. f. represents the force (magnetic pressure) 
that tends to drive the fines of force throughout the entire 
path of any kind of material. 



210 LESSONS IN PRACTICAL ELECTRICITY 

184. Law of the Magnetic Circuit. — Just as electric pres- 
sure- (E. M. F.) is the force that moves electricity through an 
electric circuit, so magnetic pressure (m. m. f.) is the force 
that drives lines of force through a magnetic circuit. All 
magnetic substances offer some opposition to the passage 
through them of magnetic lines of force. This opposition, or 
magnetic ^'resistance," is termed reluctance, the symbol for 
which is Gl. The total number of Hues of force set up in a mag- 
netic substance is termed magnetic flux. Magnetic flux, or total 
number of lines of force, is treated as a magnetic ''current" 
flowing in the magnetic circuit. 

The calculation of the magnetic flux, which we will repre- 
sent by the letter N, is similar to the calculation of current 
in an electric circuit by Ohm's Law. In an electric circuit 
the strength of the electric current equals the E. M. F. -^ resis- 

E . 

tance, that is I = — ; in a magnetic circuit the number of mag- 
R 

netic lines of force which pass through it is equal to the m. m. f . 

-^ reluctance, or 

^. ^ magnetomotive force 

magnetic flux = — , 

reluctance 

m. m. f ,_.. 

N = ^ , (71). 

This equation is analogous to the expression for Ohm's Law 
and on this account is frequently styled the "Ohm's Law of 
the magnetic circuit." 

185. Magnetic Density, Permeability and Reluctance. — It 
is sometimes necessary to specify the flux density in any part 
of a magnetic circuit, that is, the number of lines passing 
through a unit area measured at right angles to their direction, 
whether that part of the circuit is air or some other material. 
This number is termed the magnetic density or magnetic induc- 
tion of the substance, and is denoted by the letter ^. If the 
total flux N is known, and the area A through which it is uni- 
formly distributed is also known, then the flux density is 
given by 

^ = J ............... . (72). 



ELECTROMAGNETS 211 

If the area of cross section of the substance A be expressed in 
square inches or square centimeters, the flux density will be 
the number of lines per square inch or per square centimeter 
respectively. 

The magnetic density produced in air by a solenoid depends 
entirely upon the intensity of the magnetic field (\\ 183). 
The magnetic density or induction (B produced in a magnetic 
substance when placed in a solenoid depends upon one other 
factor, namely, the permeability of the substance. 

The permeability of a magnetic substance is the ratio of 
the magnetic density ^ in the substance to the intensity of 
magnetic field 3C acting upon the substance; that is, a ratio 
of the number of lines of force per unit area, set up in the 
material, to the number that would be set up in air under the 
same conditions. The symbol for permeabihty is the Greek 
letter /x (pronounced mu) , " and its value for any magnetic 
substance is expressed in the equation 

M=| (73). 

If the value of fx and !JC are known, the magnetic density is 
^ = M X X 

The .permeabihty of air or non-magnetic substances is unity 

SB 
or 1; since through air the flux density ^ = TK^,OY--r.= l. 

ji 

For soft iron under a field intensity X = 10 (this corre- 
sponds by Formula (70) to 20.3 ampere-turns per inch), the 
flux density is ^ = 14,000 fines per sq. cm., and consequently 
the permeability is 14,000 ^ 10 = 1400. 

In magnetic materials the value of the permeabihty does 
not remain the same for all flux densities; this variation of 
permeabihty is shown in Table X. 

The reluctance of a magnetic circuit depends upon three quan- 
tities: the length of the circuit, the cross-sectional area of the 
circuit, and the permeability of the material which forms the 
circuit. The reluctance increases as the length of the mag- 
netic circuit increases, and decreases as the cross-sectional area 



212 



LESSONS IN PRACTICAL ELECTRICITY 





Table X. 


Permeability ' 


rable 




Flux 


Density 


PERMEABILlTy 


Lines 


Lines 


Annealed 


Cast 


Cast 


per square 


per square 


sheet 


steel 


iron 


inch 


centimeter 


steel 






20,000 


3,100 


2600 


1400 


280 


30,000 


4,650 


2900 


1500 


230 


40,000 


6,200 


3100 


1400 


160 


50,000 


7,750 


3200 


1350 


110 


60,000 


9,300 


3100 


1250 


80 


70,000 


10,850 


2400 


1100 


65 


80,000 


12,400 


1800 


750 


50 


90,000 


14,000 


1400 


500 




100,000 


15,500 


750 


280 




110,000 


17,400 


320 


145 




120,000 


18.600 


160 


70 




130,000 


20,150 


-75 







is increased and as the permeability increases. That is, the 
rehictance is directly proportional to the length of the mag- 
netic circuit, is inversely proportional to the cross-sectional 
area, and varies with the material of the circuit. 

Letting 91 represent the reluctance, 1 the length of magnetic 
circuit in. inches, A the sectional area of the circuit in square 
inches, and /x the permeability of the material constituting the 
circuit, then 



91 



A X M 



(74). 



186. Calculation of Magnetic Circuits. — The magnetic cir- 
cuit is usually a compound one; that is, one composed of two 
or more substances; part of the magnetic path may be an air- 
gap which would materially increase the reluctance. It is, 
therefore, necessary to calculate separately the reluctance 
offered by each substance. The total reluctance is the sum 
of the separate reluctances of the various substances. Before 
the reluctance of any substance included in the magnetic 
circuit can be calculated, it is necessary to know the permea- 
bility of the substance. The permeability depends not only 



ELECTROMAGNETS 



213 



upon the kind and quality of the substance, but also upon 
the density ^ of the lines of force. The total induction (mag- 
netic flux N) and the dimensions of the magnet having been 
determined, the value of the induction ^ for each substance is 

N 
found by Formula (72), ^ = y- From a table or curve giving 

A. 

the value of ^ and "DC for different magnetic substances, the 
permeability may be calculated by taking the ratio ^ ^ TK.] or 
the permeability may be taken directly from Table X of ]f 185. 
Having determined the perrneabihty for each substance, 
the reluctance of each substance can be calculated, and then 
the total reluctance. The total reluctance 91 of the entire 
magnetic circuit having been determined, and the total num- 
ber of lines of force or magnetic flux N having been established 
in the beginning by the requirements of the magnet, it be- 
comes necessary to determine the ampere-turns required to 
drive the magnetic flux around the magnetic circuit. Since 
m. m. f. 



magnetic flux = 



dl 



the m. m. f. would equal N x ^, 



and as m. m. f. = ampere-turns X 3.2 (*f 182), it foUows that 

the ampere-turns required to drive a given 

magnetic flux through a magnetic circuit 

would equal 

N 
ampere-turns = —— X ^ .... (75). 
o.Z 

Problem 88. — Fig. 157 gives the dimensions in 
inches of a cast steel horseshoe core and keeper, | 
separated by an air gap of one-quarter of an inch; 
the dotted line represents the total length of the 
magnetic circuit. Find the reluctance of each part 
of the magnetic circuit and the ampere-turns re- 
quired to drive 40,000 lines of force through that 
circuit. 

Lengths of both limbs of core up to curved 
portion = 4.25 x 2 = 8.5 inches. Since the circum- 
ference of a circle = diam. x 3.1416, or radius 
X 2 X 3.1416, the length of the curved portion of 
the core is one-half the circumference = radius X 

3.1416 = 1.625 X 3.1416 = 5.105 inches. Then, the total length of core is 
8.5+5.105= 13.605 inches. 




Fig. 157. — Horseshoe 
Core and Keeper. 



214 LESSONS IN PRACTICAL ELECTRICITY 

Area of the round core of diameter d = 0.75 inch is d^ x 0.7854 = 0.75 
X 0.75 X 0.7854 = 0.441 sq. in. 

Induction = ^ = — = ' = 90,700 Hues of force per sq. in. 

From Table X the permeability /jl for cast steel at a flux density of 
90,700 is about 500. 

Then, reluctance of core: 

_l_^ 13.605 _^^^ 
A X M 0.441 X 500 

Reluctance of both air gaps: 

Total length of gaps = 0.5 inch (each gap 0.25 inch). 

Area of air path is taken the same as of core, namely 0.441 sq. in. 

fx for air =1. Then, 

gi=—^= Q-^ =1.133. 
A X M 0.441 X 1 

Reluctance of keeper: keeper is bent to the same radius as upper part 
of horseshoe; therefore, its length is the same as that part. The cross-sec- 
tional area of the keeper is the same as the core; therefore, the value of 
^ and permeability is the same, since it is of the same material. Thus the 
reluctance of the keeper is 

_1_^ 5.105 ^^^^3^ 
A X M 0.441 X 500 

Total reluctance = 0.062 + 1.133 + 0.023 = 1.218. 
Then, 

ampere-turns = ^-^^X (total 91) = — ^-r — X 1.218 = 15,230 ampere-turns. 

187. Magnetization Curve. — Unlike the constant resistance 
offered by a piece of copper to different strengths of an 
electric current, the reluctance of a piece of iron varies with 
each density of the lines of force accommodated through it, 
and this variation bears no constant ratio to the number of 
lines of force passing through.it. For this reason curves of 
magnetization are constructed for different specimens of iron 
showing the relation of the induction to the field intensity at 
different stages of magnetization. Fig. 158 shows magnetiza- 
tion curves of steel and iron, the curves gradually sloping 
upwards with increased exciting current until the saturation 
pomt is reached, when the curves slope off to the horizontal. 



ELECTROMAGNETS 



215 



120 



^m 



80 



60 



o 40 



^ 10 































.\pd 


5/7£!b^ 


j/ 


— 


■ — 






^ 




Sfgel 






h^ 






/I 


^^ 




^^ 












j 


/ 


X 


















/ 


















1 




















1 
















^- 


-^ 


/ 








cjs: 


LJi^ 










/ 




^ 


^ 














1 


/ 


















/ 




















/ 





















40 



ZOO 



80 120 160 

Ampere-Turns per Inch 

Fig. 158. — Magnetization Curves of Steel and Iron 

With a given magnetizing force in ampere-turns the induction 
may be found from the curves. 

188. Attractive Force of an Electromagnet. — The magnet- 
ism of an electromagnet increases as the current through it 
is increased, up to the satura- 
tion point (see H 15), but is not 
directly proportional to the cur- 
rent; that is, if one ampere 
through a certain magnet re- 
quires a force of 56 pounds to 
detach its keeper, then when 2 
amperes are passed through it, 
not twice the force, or 112 
pounds, is required, but usually Fig. 159. — Testing the Attractive 
much less. To make a test of ^^^^^^ ^^ ^^ Electromagnet, 
the effect of different current strengths upon the attractive 




216 LESSONS IN PRACTICAL ELECTRICITY 

power, the magnet and keeper may be arranged in connection 
with a spring balance and windlass, as shown in Fig. 159. 
When the crank is turned the pounds pull may be noted till 
the detachment of the. keeper takes place. 

The Ufting or adhesive power of an electromagnet is called 
its tractive force. The tractive force is proportional to the 
square of the density of hues of force per square inch, and the 
area of the surface contact. To determine the tractive force 
or ''pull," in pounds, of an electromagnet, let 

^ = flux density or hues of force per square inch, 
A = area of contact in square inches. 

Then, the pull in pounds is 

p ^ ^^x A 
72,134,000' 

For example: suppose a density of 45,000 lines of force per square 
inch to be produced in an electromagnet by the magnetizing force. What 
would be the pull required to detach its keeper if the poles of the magnet 
had a total area of 1 square inch? 

^ 2 ^ 45,0002 = 2,025,000,000; A = 1 sq. in.; then, 
Pull = 2,025,000,000 x 1 ^ 72,134,000 = 28 pounds. 

Due to magnetic leakage, that is, some of the magnetic lines 
completing their path through air instead of through the 
keeper, the actual pull will be less than the pull calculated 
above. 

QUESTIONS 

1. The pole of an electromagnet having a soft steel core deflects a 
compass needle 44 degrees when held at a distance of one foot. A soft 
iron core is substituted for the steel and the deflection is now 58 degrees. 
How do you account for this, since neither the distance nor the current 
strength is altered? 

2. -Define magnetic permeability. 

3. Which magnet core mentioned in Question 1 possesses the greater 
permeabihty? 

4. Wind a steel key ring with insulated wire so that when a current 
is sent through the windings the ring will possess two diametrically oppo- 
site poles. Illustrate by sketches the direction of winding, direction of 
current, and direction of the magnetic lines of force. What kind of poles 
are produced in the key ring? 



ELECTROMAGNETS 217 

5. What is reluctance? How does the magnetic reluctance of air com- 
pare with that of iron? 

6. The magnetomotive force of a solenoid is doubled. How would 
this affect the number of lines of force threading through it when the 
solenoid possesses a brass core? A soft iron core? 



PROBLEMS 

1. Calculate the reluctance of a non-magnetic rod 10 inches long and 
I inch in diameter. 

2. Three relays are adjusted to operate on 250 ampere- turns, and have 
the following constants: — 

Relay A — 2400 turns, 20 ohms resistance; 
Relay B — 4500 turns, 75 ohms resistance; 
Relay C — 7500 turns, 150 ohms resistance. 

If these relays were connected in series across a 20-volt battery, which 
relays would operate ? 

3. \\Tiat voltage would cause all three relays of Question 2 to operate ? 

4. Calculate the ampere- turns to be placed on a wrought-iron horse- 
shoe electromagnet to produce a flux of 100,000 lines of force through it, 
the shape of the magnet being shown in Fig. 157 and its linear dimensions 
being just double the values given in that figure. 

5. What flux density will a magnetizing force of 50 ampere-turns per 
inch produce in cast iron ? In annealed sheet steel ? 

6. Design a horseshoe electromagnet of wrought iron that will exert a 
pull of 100 pounds when traversed by a current of 2 amperes. 



LESSON XV 



ELECTRODYNAMICS 

Reaction of a Current-carrying Wire on a Magnet — Automatic Twist- 
ing of a Current-carrying Wire around a Magnetic Pole — Rota- 
tion of a Ciu-rent-carrying Wire around a Magnetic Pole — Elec- 
trodynamics — The Magnetic Fields of Parallel Currents — Laws of 
Parallel Currents — Currents in Conductors at an Angle with Each 
Other — Questions. 

189. Reaction of a Current-carrying Wire on a Magnet. — 

Every action is accompanied by an equal and opposite re- 
action, or, " action and reaction are equal and opposite." 
For example, elongate a spring in one direction by applying 
a force of one pound; the spring also exerts an equal force in 
the opposite direction, or else it would break. A ship dis- 
places an amount of water which is equal to its own weight; 

the force of buoyancy is, therefore, 
equal and opposite to the weight 
of the ship, or else it would either 
rise or sink until equilibrium is 
established. 

In Lesson XIII it was shown 
how a magnet was deflected by 
the field of a wire carrying a cur- 
rent. When the current flows 
over the needle, say from north to 
south, and the needle is free to 
move, the N-end is urged by the 
for Determining the Direction of current's field to the east and the 
Rotation o^ a Moving Wire in a S-end, to the west. Since the field 

of the wire reacts on the magnet's 
field, the magnet's field also reacts 
on the field of the wire, and if the wire were free to move, it 
would deflect in the opposite direction to that of the magnet. 

218 



left Hand 




Fig. 160. — Left-hand Rule 



Magnetic Field 

This rule applies to motors 



ELECTRODYNAMICS 



219 



In ^168 the right-hand rule was given for the direction of the 
magnetic hnes around a wire or the direction in which the 
needle would turn. Th3 following rule employing the left 
hand will indicate the direction that the wire will naove when 
the magnet is stationary. 

Place the thumb, first and second fingers of the left hand all at 
right angles to each other, as in Fig. 160, and the hand so that 
the first finger indicates the direction of the lines of force of the 
magnet and the second finger the 
direction of the current in the wire; 
the thumb will then indicate the 
direction of motion of the wire. 

Experiment 71. - — Insert a rectangular 
coil having a single turn of wire in a suit- 
able frame as shown in Fig. 161. Place 
the horizontal portion of the coil in the 
magnetic meridian, and by the use of a 
pocket compass find the direction of cur- 
rent around the wire. Open the circuit 
and lay a bar magnet on the base, ar- 
ranged so that the current flows over it 
from north to south, as in Fig. 161. The 
magnet is now stationary and the wire 
free to move. When the current flows 
the wire is deflected west. Apply the 
left-hand rule just given to this case. 

Experiment 72. — Explore the mag- 
netic field both inside and outside of the rectangular coil by noting how 
the wire moves when the magnet is brought into its vicinity. The wire 
tends to move in all cases to such a position that its o\\ti lines of force 
are in the same direction as those of the field of the magnet. 




Fig. 161. — The Movable Cur- 
rent-carrying Coil is Repelled by 
the Stationary Bar Magnet. 



190. Automatic Twisting of a Current-carrying Wire 
around a Magnetic Pole. — That a wire tends to move so that 
its magnetic field will be in the same direction as the lines of 
force of the magnet's field is further demonstrated as follows: 
a bar magnet is clamped vertically in a stand and raised several 
inches from the table (Fig. 162), a connector is clamped above 
it, and a piece of tinsel wire (which is a very flexible conductor) 
is supported from the connector and joined to a battery. 
When the current is sent up the wire from A to B, the wire 
twists or winds itself around the magnet in a left-hand spiral, 



220 



LESSONS IN PRACTICAL ELECTRICITY 




so that the current circulates around the magnet anti-clock- 
wise as viewed from the N-pole end. The current, therefore, 
tends to increase the magnetism of the 
magnet and the lines of force of both are 
in the same direction. When the current 
is reversed, the tinsel unwinds and again 
twists itself around the magnet in a right- 
hand spiral, or so that the polarity of the 
magnet is increased by the current's field 
as before. 

191. Rotation of a Current- carrying 
Wire around a Magnetic Pole. — Since 
the tendency of a magnet is to urge a 
wire carrying a current to a position at 
right angles to it, continuous rotation of 
the wire can be produced if the wire be 
arranged free to move in such a manner 
that it will never attain such a position. 
In Fig. 163 a wooden ring, with a groove 
turned in it for 
the reception of 
mercury, is 
mounted above 
an electromagnet. One end of a piece 
of copper wire, AB, is hooked onto the 
stationary horizontal brass arm, which 
is supported by the vertical rod as de- 
picted. The other end of the copper 
wire dips into the mercury trough which 
serves to complete the circuit of the 
current through the electromagnet. 

The magnetic field of the electromag- 
net is nearly at right angles to the wire, 
and the wire rotates about the pole 
when the current is passed through it. 
The direction of rotation can be deter- 
mined before the current is turned on by the left-hand rule of 
If 189. Applying this rule we find that the wire will rotate in 
the direction opposite to the hands of the clock. It tends to 



Fig. 162. — The Flex- 
ible Tinsel Wire Winds 
around tHe Magnet 
when a Current is Sent 
through It. 




Fig. 163. — Rotation of 
a Current-carrying Wire 
around a Magnet Pole. 



ELECTRODYNAMICS 



223 



wind around the pole in such a direction as to increase the mag- 
netism of the pole, just as in the '^automatic twisting" experi- 
ment (If 190). 

This rule is very convenient for determining the direction of 
rotation of motors (If 284). The moving wire in Fig. 163 is 
analogous to the armature t)f the motor, and the electromagnet, 
its field. If the direction of current through the armature and 
field of Fig. 163 be reversed, as by changing the binding post 
terminals, the direction of rotation will be the same as before, 
because the current through the moving wire and the polarity 
of the field are both reversed, therefore, the same relation 
exists as before, which can be proved by the left-hand rule. 
If, now, only the current in the wire be reversed, or only the 
polarity of the field, then the direction of rotation will be 
reversed. Therefore, to reverse the direction of rotation of a 
motor, reverse the direction of current either through the arma- 
ture or through the field 7nagnets, hut not through both. 

A permanent magnet can be substituted for the electro- 
magnet in Fig. 163, as the same principles are involved. The 
wooden ring could be lowered ■ to the middle position of the 
magnet and the wire prolonged, in which case a greater part 
of its field would be in the magnet's field. If the ring were 
located on the base (Fig. 163) and the wire, AB, extended the 
whole length of the magnet, 
one pole would tend to urge 
it in one direction and the 
other pole in the opposite 
direction, so that with the 
poles of equal strength the 
wire would not rotate. 

Another device to produce 
continuous rotation is illus- 
trated in Fig. 164, and is 
called Barlow s wheel. The 
edge of a pivoted copper disk dips into a trough of mercury, C, 
located between the poles of a horseshoe magnet, and current 
is sent through the disk in a radial direction, as shown. The 
magnet's field acts at right angles to the current's field, since 
the current flows from the periphery of the disk to its axis, A, 




Fig. 164. — Barlow's Wheel. 

Faraday's disk dynamo driven as a motor. 



222 



LESSONS IN PRACTICAL ELECTRICITY 



and the disk will rotate in the direction of the hands of a 
clock (Fig. 164) ; this statement can be verified by the left-hand 
rule. 

192. Electrodynamics. — The term electrodynamics is ap- 
plied to the study of that part of electricity which treats of 
the force exerted by one current upbn another. We have just 
noted the reciprocal action between a current and a magnet, 
and now in electrodj^namics, the mutual action of the currents 
upon each other is to be considered. Every wire through 
which a current is flowing is surrounded by a magnetic field, 




-N N 






,N N, 



^\W 



Reput; 




Attraction 



Fig. 165. — Parallel Currents Flowing in the Same Direction Attract 
Each Other; if in Opposite Directions they Repel Each Other. 

and the magnetic fields of two wires react upon each other. 
This, reaction may take place between two neighboring wires 
in the same circuit through which a current is flowing, or it 
may occur between wires in two independent circuits, the 
action depending on the relative directions of the two mag- 
netic fields. 

193. The Magnetic Fields of Parallel Currents. — The 
magnetic field of a straight wire carrying a current was illus- 
trated in Fig. 124. If, for convenience, you regard magnetic 
lines as being of N-polarity when their direction is toward you, 
and of S-polarity when their direction is away from you, then 



ELECTRODYNAMICS 



223 



when the direction of the whirls is kept in mind, the N- and 
S-polarity of a straight wire may be readily remembered. In 
the left-hand diagram of Fig. 165 the direction of the current, 
the direction of whirls and polarity of the wire are indicated. 
The wires pass through a piece of cardboard upon which, by 
the aid of iron filings, the graphical field is made. The current 
in the parallel wires flows in opposite directions, so that the 
two adjacent sides 



^ 




Tinsel 



N N 





Tinsel 
L. Wire 




are of the same 
polarity, thus caus- 
ing a force of repul- 
sion to exist between 
them. The wires 
tend to move away 
from each other. 
The field is very 
condensed between 
the wires and elon- 
gated outside of 
them. Midway be- 
tween the wires the 
lines of force are in 
the same direction 
and are perpendicu- 
lar to the plane of 
the loop of wire. The repulsion between the wires may be 
demonstrated by the following experiment. 

Experiment 73. — Support a wire connector and suspend therefrom two 
long, parallel pieces of tinsel wire arranged close to each other, and con- 
nect them to a source of current as shown at A of Fig. 166. When the 
circuit is closed the currents, being in opposite directions, repel each other 
and the wires move apart as depicted, according to the principle just 
stated. 

In the right-hand diagram of Fig. 165, the currents in the 
parallel wires are in the same direction and the polarities of the 
adjacent wires unlike, so that attraction results according to 
the law for unlike polarities. This is noted in the filing dia- 
gram, where the field on the outside of the wires is very much 
condensed and elongated between these wires. There are also 



Fig. 166. — Repulsion and Attraction between 
Suspended Tinsel Wires Carrying Currents. 

A — Currents in opposite directions — repulsion 
B — Currents in the same direction — attraction. 



224 



LESSONS IN PRACTICAL ELECTRICITY 




Fig. 167. — Repulsion and Attrac- 
tion between Parallel Currents. 



continuous curves embracing both wires, due to the unison 
of some of the magnetic Hues of both wires. The wires tend 

to be drawn together by the 
tension along these lines of 
force. This attraction is demon- 
strated in Experiment 74- 

Experiment 74 . — Pass the current 
through the two parallel tinsel wires 
in B (Fig. 166) in the same direction. 
Although the wires were originally 
separated by some distance they move 
toward each other. 

194. Laws of Parallel Cur- 
rents. — 1. Parallel wires 

CARRYING CURRENTS FLOWING 
IN THE SAME DIRECTION AT- 
TRACT EACH other; but if 

THE CURRENTS ARE IN OPPOSITE 
DIRECTIONS THEY REPEL EACH 

OTHER. See Fig. 167. This law is true for wires of independent 
circuits or for two parts of the 
same circuit. 

2. The force between two 
parallel currents is pro- 
portional to the product of 
the current strengths and 
to the length of the wires 
considered, and varies in- 
versely as the distance be- 
tween them. 

The first law may be further 
demonstrated by the Ampere- 
frame coil shown in Fig. 168. 

Experiment 75. — Connect the 
Ampere-frame coil and another coil in 
series to a source of current (Fig. 
168). Trace the direction of current 
in each coil. Hold one side of the rectangular coil, CD, parallel and close 
to one side of the movable coil, AB. The wke AB is repelled and moves 




Fig. 168. — The Movable Coil 
(A B) may be Attracted or Repelled 
by the Stationary Coil (CD). 



ELECTRODYNAMICS 



225 



Spiral 

Wire 



away from CD when the currents are in oppo&'ite directions (Fig, 168). 

Invert the ?oil CD so that the cur- 
rent flows in the same direction 

through both, and the movable c^oil 

is attracted and will follow CD if it 

is carried around the axis of the coil 

AB. 

Experiment 76 : Roget's Jumping 

Spiral. — A further demonstration 

of the first law employs a phosphor 

bronze spring, S, supported verti- 
cally by a stand (Fig. 169). The 

lower end dips into a cup of mer- 
cury, C. Current is passed through 

the spring and flows around each 

convolution in the same direction, 

hence the magnetic fields of all the 

convolutions attract each other, and 

the length of the spiral is shortened 

to such an extent that the lower end 

is pulled out of the mercury cup, 

thus breaking the circuit. Gravity 

now pufls the spring down again 

and the circuit is reestablished, only 

to be broken by the same action. 

The spring thus vibrates continu- 
ously like the vibrator of an electric 

bell. An iron rod lowered through the 
center of the spiral, so that it does not 
touch the convolutions, greatly increases 
the action by increasing the magnetic 
effects of the whirls around each w^ire. 

In any solenoid or electromag- 
net, the magnetic field, therefore, 
tends to bind the wires closer 
together, as in Roget's spiral, 
since the current is in the same 
direction through all the turns, 
and all the convolutions are 
Fig. 170. — Attraction and parallel. The windings of elec- 
Repulsion between Currents trical machines and apparatus 
Flowing at an Angle to Each ^^^^ ^^ designed to withstand 

the forces due to the currents in 
those coils, even under short-circuit conditions. 




Roget's Jumping Spiral. 



It illustrates the law of parallel currents 
flowing in the same direction. 




226 



LESSONS IN PRACTICAL ELECTRICITY 



195. Currents in Conductors at an Angle with Each Other. — 

In Fig. 170 two insulated wires AB and CD make an angle 
with each other, and the currents flow from A and C toward 
P, and the portions AP and CP attract each other. This is 
indicated by the polarity of the wires and the direction of 
the whirls around them. Currents also flow away from P, 
toward B and D, and similar attraction takes place. Now 
consider the current and polarity in the part of the wire AP 
and PD. In AP the current flows toward P and in PD away 
from P, and repulsion exists as indicated. These facts are 
summarized by the following law: 

Two WIRES CROSSING EACH OTHER AT AN ANGLE ATTRACT 
EACH OTHER IF THE CURRENTS IN BOTH OF THEM FLOW EITHER 

TOWARD THE POINT OF CROSSING 
OR AWAY FROM IT; BUT THEY 
REPEL EACH OTHER WHEN THE 
CURRENT FLOWS TOWARD IT IN 
ONE WIRE AND AWAY FROM IT 

IN THE OTHER. The motiou 
tends to make the wires not 
only parallel, but also coinci- 
dent. This law is very impor- 
tant, and upon its principle are 
constructed electro-dynamom- 
eters and wattmeters (^214, 
11223, etc.). This law can be 
Fig. 171. — Angular Currents demonstrated by the apparatus 
i'nThe WDTeftS"'' '"' ^'°" described in Experiment 77. 

Experiment 77. — Inside of the movable rectangular coil AB (Fig. 
171) is clamped a fixed coil CD. The two coils may be connected in series 
or to two independent circuits. The movable coil AB is turned so that its 
plane makes an angle with the plane of the coil CD. If the current be sent 
through the coils so that it flows along AB and CD either toward or away 
from their angle of intersection, the coil AB will move in the direction 
of the arrows till its plane coincides with that of CD, or till they are parallel, 
according to the foregoing law. If, now, the current through either but 
not both of them be reversed, the coil AB will move against the direction 
of the arrows and complete one-half revolution, till its plane coincides 
with CD, when B will be directly above C. This motion is in accordance 
with the latter half of the law which applies when the currents flow in one 
wire toward the point of crossing, and in the other wire away from it. 




ELECTRODYNAMICS 227 



QUESTIONS 

1. Two parallel wires are stretched from vertical supports, the meas- 
tired distance between them being 2 inches. A current is sent through 
the wires, and the distance is now only If inches. How do you explain 
this? 

2. If the current is reversed in both wires in Question 1, how will they 
now be affected? 

3. Two wires cross each other at an angle of 60° and the current flows 
through them in opposite directions. Will they tend to move so as to 
increase or decrease the angle of crossing? 

4. A vertical wire carrying a current rotates around the S-pole of a 
magnet in a direction against the hands of a clock as viewed from the 
S-pole end. Is the current flowing up or down the wire? 

5. A copper disk is mounted between the poles of a horseshoe magnet 
and current is passed from its center to the circumference. Make a sketch 
indicating the direction in which the disk will rotate. How can you 
change the direction of rotation of the disk? 

6. Current is passed downward through a vertical wire, and a bar mag- 
net with its N-pole held uppermost is placed near to and parallel with the 
wire. Suppose the magnet to be flexible, Hke a piece of tinsel wire, what 
will occur? Make a sketch. 



LESSON XVI 
GALVANOMETERS 

Principle of the Galvanometer — Detector Galvanometer — Sensibility of 
a Galvanometer — Shunts — Tangent " Galvanometer — Tables XI 
and XII — Thomson Galvanometer — Reading Devices for Mirror- 
type Galvanometers — Astatic and Differential Galvanometers — 
D'Arsonval Galvanometer — The BaUistic Galvanometer — Ayrton 
Shunt — Questions and Problems. 

196. Principle of the Galvanometer. — An instrument which 
measures a current by one of its effects is called a galva- 
nometer. Galvanometers are used for detecting the presence 
of an electric current in any circuit, and for determining its 
direction and relative strength. Their construction is based 
on the principles: 1, that a magnetic needle is deflected when 
brought under the influence of a magnetic field produced in 
the neighborhood of a wire through which a current is flowing, 
or 2, that a coil suitably located between the poles of a per- 
manent magnet will be deflected when a current traverses that 
coil. According to these principles of action, galvanometers 
may be divided into two classes: first, those in which the 
magnet or magnetized body is arranged to move and the coil 
held stationary, and second, those in which the magnet is 
stationary and the coil arranged to move. Each class is largely 
used in practice for laboratory and commercial purposes, and is 
constructed in a variety of forms. The method of supporting 
the moving system may be either by suspension, by poising 
it, or by delicate springs. The deflections may be noted either 
by a pointer attached to the system and moving over a gradu- 
ated scale, or by a small mirror attached to the system. In 
the latter case, a ray of light falling upon the mirror is reflected 
upon a scale at some distance and greatly enlarges a small 
movement of the moving system. In another method the 

228 



GALVANOMETERS 229 

image of the scale deflection is observed on the mirror by a 
telescope located at about the same distance as the scale 
(11202). 

A simple galvanometer consists essentially of a magnetic 
needle poised or suspended in the center of a coil of wire and 
provided with a circular scale, graduated in degrees, on which 
the deviation, or deflection, of the needle may be noted. When 
such an instrmnent is connected in a circuit the presence of 
the current therein is shown by the deflection of the needle. 
The direction of the current is shown by the side towards 
which the N-pole of the needle moves (T[ 167), and the strength 
of current is indicated by the amount of the deflection. The 
position that the needle takes up depends upon the relative 
magnitudes of the magnetic field due to the current and of 
the field due to the earth; it will point in the direction of the 
resultant of these magnetic fields. The earth's magnetism 
may be considered to be approximately constant at any par- 
ticular place. 

To obtain the maximum effect of the current's field, the 
galvanometer wire or coil, when no current is flowing, is ar- 
ranged parallel to the magnetic needle when it is at rest, so 
that the plane of the coil passes through the axis of the needle 
and the magnetic meridian. Such galvanometers are usually 
set up to conform to the above conditions before sending a current 
through them. The greatest possible deflection of the needle 
is then 90 degrees, which places it at right angles to the coil. 
The value of the deflection is dependent upon the current 
flowing through the coil, but is not proportional to the cur- 
rent; that is, if one current produces twice the deflection of 
another current the former is not of double the strength. With 
the needle parallel to the coil, or at the zero scale position, a 
small current deflects it considerably, but as the angle the 
needle makes with the coil increases, a much greater magnetic 
force is required. For example, it requires a greater current 
to deflect the needle one degree from the 45-degree position 
than to deflect it one degree from the 15-degree position. The 
galvanometer coil may be wound with a great many turns of 
fine wire, in which case the instrument is said to be sensitive 
(that is, the needle is appreciably deflected by a very small 



230 



LESSONS IN PRACTICAL ELECTRICITY 




Fig. 172. — Student's 
Detector Galvanometer. 



current), or it may be composed of a few turns of very heavy' 
wirC; in which case it is intended for use with large currents 
197. Detector Galvanometer. — A student's detector gal- 
vanometer is illustrated in Fig. 172, and the parts in Fig. 173. 
A circular glass-covered box contains 
the magnetic system inclosed in a rec- 
tangular coil wound with small wire 
An aluminum pointer is fixed to an 
aluminum cap (Fig. 173) and the mag- 
netic needle fastened to a glass jewel. 
The cap telescopes the jewel and the 
pointer is arranged at right angles to 
the needle. One-half of the dial is 
graduated in degrees and the other half 
in divisions corresponding to the tan- 
gents of the various angles (H 200). In adjusting this instru- 
ment for use, turn the box around 

till the pointer is directly over the ^^^ 

zero mark on the scale; the pointer 
will then point east and west, and 
the magnetic needle at right angles 
to it will be in the magnetic meri- 
dian, as will also the coil of wire. 
The coil is wound with No. 30 B. & 
S. magnet wire, and has a resistance 
of about 30 ohms. The instrument 
is quite sensitive; a current of about 
0.00001 ampere will deflect the 
needle 1 degree from its position of 
rest. 

In measuring the resistance of the --- ^^^'^'^ 

insulation around a piece of wire o. ^i^^" i^^AT ^^^^/?^,^*^°^^^ 
/T-i- ArjA\ X • ^ p Student s Detector Galvanom- 

(Fig. 174), a current is passed irom eter. 

a sheet of tinfoil, wrapped around 

the insulated wire, through the cotton insulation to the wire 
itself. The value of this current is to be noted on the galva- 
nometer in the circuit. The current that flows through this in- 
sulation will be very small, so that the galvanometer must be 
extremely sensitive to record such a minute current. For this 




GALVANOMETERS 



231 



■Sm'fch 



Oalvanomefer 



purpose a galvanometer of the type illustrated in Fig. 172 should 
have a coil small in diameter and wound with many turns of 
very fine wire, and the needle must be delicately pivoted to 
eliminate as much friction as possible. 

On the other hand, suppose it is desired to indicate the 
current flowing through a number of incandescent lamps. 
If the foregoing galvanometer is connected in series with the 
lamps, its resistance would be so high that the lamps would 
not light, or the coil might be destroyed due to an excessive 
current passing through it. A galvanometer having a coil of 
large diameter and of few turns, and consequently of very low 
resistance, is suitable for this case. 
The total magnetizing force deflect- 
ing the needle may be the same as 
before, but is now produced by a 
large current circulating around a 
few turns, instead of a small current 
around thousands of turns {\ 182). 

Galvanometers of high resistance 
are used to measure electrical pres- 
sure and, when properly standard- 
ized, their scales are graduated to 
read directly in volts; the instru- 
ment then becomes a voltmeter 
(11216). 

sists in experimentally determining 
the position of the needle, when the coil is subjected to different 
known pressures, and marking these values on the scale; the 
process is called calibration. It is still the current that deflects 
the needle but its strength is dependent upon the pressure. 
Galvanometers of very low resistance may have their scales 
calibrated to read directly in amperes, and thus become am- 
pere-meters or ammeters (^ 207). 

198. Sensibility of a Galvanometer. — The sensitiveness of 
a galvanometer may be expressed by the amount of current 
required to produce a given deflection. The sensibility may 
also be indicated by the resistance which is placed in the gal- 
vanometer circuit so that one volt shall produce a certain de- 
flection. For example, a galvanometer with a '' sensibility of 




Battery 



The standardization con- ^'^- ^^f: -Measuring Insula- 

tion Resistance. 



^D 



232 LESSONS IN PRACTICAL ELECTRICITY 

2 megohms," means one in which the movable system will be 
deflected one division of the scale when it is connected in series 
with 2 megohms under a potential difference of 1 volt appHed 
to the circuit. 

The sensibihty of a galvanometer depends upon the number 
of times the current circulates around the coil, the distance of 
the needle from the coil, the weight of the needle, and the 
amount of friction produced by its movement. The needle is 
usually quite small, and often a compound one. In very sensi- 
tive galvanometers of the moving-coil type the coils are wound 
with thousands of turns of very fine wire and the permanent 
magnets are strongly magnetized. 

199. Shunts. — If the current passing through the galva- 
nometer (G, Fig. 175) is too large, only a fraction of the total 
. current should be passed through the 

^\AA — V galvanometer, the remainder passing 

through the wire S, connected across 
the galvanometer terminals. The wire 
S forms a '^ by-path" for the current, 
and is called a shunt, and the galvanom- 
eter is said to be shunted. If the re- 
sistance of the galvanometer is 1 ohm 
and that of the shunt 1 ohm, then as 
much current will flow through the shunt 
as through the galvanometer. If the 
^'^Gahfa^iSr.*^'^ resistance of the galvanometer is 2 ohms 
and that of the shunt 1 ohm, then twice 
as much current will flow through the shunt as through the 
galvanometer; that is, the galvanometer reading must be mul- 
tiplied by 3 to obtain the total current flowing from the bat- 
tery. The value 3 is called the multiplying power of the shunt; 
it is the amount by which the shunt multiplies the range of the 
galvanometer. Any galvanometer (ammeter or voltmeter) may 
have its range of indication increased by shunting it. 
Let G = galvanometer resistance, 
S = shunt resistance, 
I = total current in the joint circuit, 
Ig = current in the galvanometer circuit, 
Is = current in the shunt. 



I9 



s 

^ AVWWWWVV — ^ 



GALVANOMETERS 233 

Then the voltage across the galvanometer is the product of its 
resistance and current, or is G X Ig; and similarly the voltage 
across the shunt is S x Is. Since these voltages are equal for 
resistances connected in parallel, it follows that 

G X Ig = S X Is 
But Is = I - Ig, therefore, 

G X Ig = S X (I - Ig) = S X I - S X Ig, 

or, by adding S X Ig to both sides of the equation, its value 
is unaltered and 

G X Ig + S X Ig = S X I, 

(G + S)Ig = S X I. 

The multiplying power of a shunt is the ratio of the total 

current, I, flowing in the circuit to that part of it, Ig, which 

flows through the galvanometer. This ratio from the last 

equation is 

,,. , . I G + S G , 

multiplymg power = :p- = — 5 — = - + 1. 

Ig b S 

1. To FIND THE MULTIPLYING POWER OF A SHUNTED GAL- 
VANOMETER : 

Divide the galvanometer resistance hy the resistarice of the 
shunt and add one to the quotient. 

Multiplying power of a shunt n = — + 1 (76), 



Problem 89. — Find the number by which the readings on a Weston 
voltmeter must be multiplied (or the mul- 
tiplying power of the shunted galvanometer) y^"| \ ^'"SOOOOhms 
in Fig. 176, when the resistance of the volt- 
meter (galvanometer) is 5000 ohms, and the 
resistance of a shunt placed across its ter- 
minals is 500 ohms. 

By Formula (76) 



„=9 + i.'™ + i. 10 + 1 = 11. 

S 500 



r<!> 



-m^ 



500 Ohms 



WW 



The readings are to be multiphed by 11 p-^ 176. -Current through 
to obtain the true value of the total current ^ Shunted Galvanometer, 
flowing. 

2. To FIND THE CURRENT, Ig, FLOWING THROUGH A 



234 



LESSONS IN PRACTICAL ELECTRICITY 



SHUNTED GALVANOMETER WHEN THE TOTAL CURRENT, I, 
FLOWING THROUGH THE CIRCUIT IS KNOWN: 

Divide the total current by the ratio of the galvanometer resis- 
tance to the shunt resistance, plus one. 

1 



Ig 



(77). 



+ 1 



Problem 90. — If 0.3 ampere flows from the battery in Fig. 176, when 
the galvanometer resistance is 5000 ohms and that of the shunt is 500 
ohms, what cm-rent will flow through the galvanometer? 

By Formula (77) 

T I 0-3 0.3 ^^_ 

^^=^- = 5-005— =ii=^-'''""P^^^' 



s-^^ 



500 



+ 1 



3. To FIND THE VALUE OF SHUNT RESISTANCE TO GIVE A 
CERTAIN MULTIPLYING POWER: 

Divide the galvanometer resistance by the multiplying power 
desired, minus one. 
Then, 

« = ^---- ('«)• 

Problem 91. — What must be the resistance of a shunt to give a multi- 
plying power of 100, when used with a galvanometer of 5000 ohms resis- 
tance? 

By Formula (78) 

G 5000 5000 „^ , 

S = = = --— = 50.5 ohms. 

n - 1 100-1 99 

Shunt boxes for galvanometers have 
several coils whose resistances are cal- 
culated to give such ratios of n as 10, 
100 and 1000. These coils may be ar- 
ranged, as a plug box, similar to Fig. 
67; by withdrawing the plugs any par- 
ticular shunt can be quickly connected 
to the galvanometer. The multiplying 
power is stamped on the box to corre- 
spond with each plug. This shunt box 
can only be used with the galvanometer (ammeter or volt- 




Fig. 177. — Shunt Box. 



GALVANOMETERS 235 

meter), for which it was calculated. Another form of shunt 
box, called an Ayrton shunt ( If 206) may be used with any 
galvanometer; it is illustrated in Fig. 177. 

200. Tangent Galvanometer. — The tangent galvanometer 
consists of a circular coil of one or more turns of large diameter 
with a short magnetic needle poised at its center. It is called a 
tangent galvanometer because a particular function of each 
angle of the needle's deflection, called a tangent, is directly 
proportional to the current flowing through the instrument. 
There is, therefore, a direct law between the current and de- 
flection when the instrument is properly constructed. The 
magnetic needle should be very small as compared with the 
diameter of the coil (for example, needle 0.75 inch long, diame- 
ter of coil 8 inches) so that the poles of the needle will be near 
the center of the coil where the magnetic field is practically uni- 
form. The axis of the needle is parallel to the coil when no cur- 
rent is flowing, both being, therefore, in the magnetic meridian, 

instead of measuring an angle in degrees of an arc, it may be reckoned 
by some function of the angle. In Fig. 178 the position of the galvanome- 
ter needle when pointing to zero on the circu- 
lar scale is represented by the line AB. Draw 
an indefinite line AF, perpendicular to AB, and 
tangent to the circle at point A. Suppose the 
needle is now deflected by the current to a point 
along the line BC, making the angle ABC of a 
certain number of degrees. The line AC is pro- 
portional to the tangent of the angle ABC. The 
value of this tangent increases as the angle opens 
out or increases; thus, if another current de- 
flects the needle along the line BD, making the 
angle ABD of so many more degrees, the tangent 
of this angle is represented in value by the length 
of the line AD. When AD is equal to AB the 
value of the tangent, which is fully defined as 
the ratio of AD to AB, is unity, and the angle 
ABC is 45 degrees. When the needle is deflected Fig. 178. — The Tangent 
at right angles, or 90 degrees, the radius pro- of an Angle, 

longed will not intersect the tangent Une, or 

the tangent of 90 degrees is infinity. The values of the tangents vary 
from to infinity. The value of the tangent for each degree of angle is 
given in the following table. For example, the tangent of 60 degrees is 
1.7321, which means that the length of the line AD is 1.7321 times as 
great as the radius AB 




236 



LESSONS IN PRACTICAL ELECTRICITY 









Table 


XI. Natural Tangents 






Angle 


Tan 


Angle 


Tan 


Angle 


Tan 


Angle 


Tan 


Angle 


Tan 


0° 


.0000 


18° 


.3249 


36° 


.7265 


54° 


1.3764 


72° 


3.0777 


1 


.0175 


19 


.3443 


37 


.7536 


55 


1.4281 


73 


3.2709 


2 


.0349 


20 


.3640 


38 


.7813 


56 


1.4826 


74 


3.4874 


3 


.0524 


21 


.3839 


39 


.8098 


57 


1.5399 


75 


3.7321 


4 


.0699 


22 


.4040 


40 


.8391 


58 


1.6003 


76 


4.0108 


5 


.0875 


23 


.4245 


41 


.8693 


59 


1.6643 


77 


4.3315 


6 


.1051 


24 


.4452 


42 


.9004 


60 


1.7321 


78 


4.7046 


T 


.1228 


25 


.4663 


43 


.9325 


61 


1.8040 


79 


5.1446 


8 


.1405 


26 


.4877 


44 


.9657 


62 


1.8807 


80 


5.6713 


9 


.1564 


27 


.5095 


45 


1.0000 


63 


1.9626 


81 


6.3138 


10 


.1763 


28 


.5317 


46 


1.0355 


64 


2.0503 


82 


7.1154 


11 


.1944 


29 


.5543 


47 


1.0724 


65 


2.1445 


83 


8.1443 


12 


.2126 


30 


.5774 


48 


1.1106 


66 


2.2460 


84 


9.514 


13 


.2309 


31 


.6009 


49 


1.1504 


67 


2.3559 


85 


11.430 


14 


.2493 


32 


.6249 


50 


1.1918 


68 


2.4751 


86 


14.301 


15 


.2679 


33 


.6494 


51 


1.2349 


69 


2.6051 


87 


19.081 


16 


.2867 


34 


.6745 


52 


1.2799 


70 


2.7475 


88 


28.636 


17- 


.3057 


35 


.7002 


53 


1.3270 


71 


2.9042 


89 


57.290 



When it is desired to compare the relative strength of two 
currents, each is passed through the tangent galvanometer, 
properly set up, and the corresponding deflections noted. The 
first current will bear the same relation to the second current 
that the tangent of the first angle bears to that of the second 
angle. The values of the tangents are taken from the table. 
Calling I and Ii the two currents to be compared and d and di 
the deflections in degrees produced by these currents respec- 
tively, then: 

I is to Ii as tan of d is to tan of di, 

IiXtand - (79). 



or 



I = 



tan di 



Problem 92. — A tangent galvanometer is deflected 17° when inserted 
in series with a solenoid and a DanieU cell. When a Grenet cell is sub- 
stituted the deflection is 31°. What is the relative strength of current 
through the solenoid when the Grenet cell is used? 

Here d = 17° tan d = 0.3; and di = 31°, tan di = 0.6. 



GALVANOMETERS 



237 



By Formula (79) 

Ii X tan d 



I 



tan di 



Ii X 0.3 

0.6 ' 



l-,lu 



or the current delivered by the Grenet cell was twice as strong as the 
current from the Daniell cell. 

Problem 93. — If one ampere deflects the needle of a tangent galvanom- 
eter 5° how many amperes will deflect it 50°? 

In this case 1=1 ampere, . d =5'', tan d = 0.0875, di = 50°, tan di 
= 1.1918. 

From Formula (79) 

I X tan di 1 X 1.1918 



Ji = 



tan d 



0.0875 



= 13.6 amperes. 



If a tangent galvanometer is constructed or adjusted so that 
one ampere deflects the needle 45°, since the tangent of 45° 
equals one, the value of the tangent of any other angle of de- 
flection will represent the value of the current in amperes 
passing through the instrument. 

For many laboratory measurements the combination tangent galva- 
nometer, illustrated in Fig. 179, may be used. It consists of the detector 
galvanometer (described in ^ 197) placed in position in the tangent coil 
frame, 8 inches in diameter, constructed of hard 
wood and mounted on a suitable base. When 
placed in position its needle is in the center of 
the coils on the frame, and the three brass level- 
ing screws underneath the base are used to level 
the instrument so that the glass jewel rides freely 
on its pivot. There are four coils of No. 18 B. & 
S. wire on the frame, each with 2 turns per coil. 
The terminals of each coil are connected to bind- 
ing posts; the figure shows the binding posts of 
two coils, the other four posts being on the op- 
posite side. Fig. 180 shows a diagram of the 
method of winding, also the method of connecting 
the four coils in series. The coils are all wound 
in the same direction, B representing the begin- 
ning of a coil and E its ending. The advantage 
of the separate coils is that they can be con- 
nected in series-parallel or multiple-series; so that the magnetic effect 
upon the needle can be altered by varying the number of turns on the 
galvanometer. Deflections may be read from the degree scale of the in- 
strument and the tangents obtained from the table, or the deflections on 
the tangent scale may be read directly since they are proportional to the 
current. The resistance of the four coils connected in series is 0.165 ohm, 
and a current of 0.25 ampere through them will deflect the needle 45*^. 




Fig. 179. — Student's 
Tangent Gavanometer. 



238 



LESSONS IN PRACTICAL ELECTRICITY 




Experiment 78. — Send a current of known strength, say 0.5 ampere, 
around one coil of the galvanometer, and note the deflection on the tan- 
gent scale. The current flows twice around the needle, since there are 
two turns per coil. Pass the same strength of current through two coils 
in series. The current flows four times around the needle and it is de- 
flected to a value on the tangent scale double that of the j&rst case. If 

three coils are used in series the tangent 
scale value is tripled. Note also the de- 
gree scale deflections, and compare the 
value of the tangents taken from the 
table for each deflection. 

The sensibility (H 198) of the 
galvanometer is, therefore, directly 
proportional to the number of con- 
volutions of wire on the coil. If 
the coil had been increased to 
twice the diameter and the same 
current had been passed twice 
around it, the tangent of the angle 
of deflection would have been just 
one-half that produced by the 
same current flowing twice around 
the smaller coil; therefore, the sensibility is also inversely pro- 
portional to the diameter of the coil, that is, decreasing the 
diameter increases the sensibility, and vice versa. 

The value of any current sent through the tangent galva- 
nometer may be calculated directly in amperes from the follow- 
ing formula, when the dimensions of the instrument are known. 
The needle is supposed to move in a horizontal plane and not 
controlled by any force other than the earth's magnetism. 

Let I = current in amperes, 

r = radius of coil in inches, 
N = number of turns in the coil, 
d = angle of deflection of the needle in degrees, 
H = a constant from the table on the next page, which 
takes care of the horizontal force of the earth's magnetism at 
the place where the galvanometer is used. 
Then 

I = ^LpXtand , . (80). 



Fig. 180. — Winding Diagram 
of Tangent Galvanometer. 

The four coils are shown connected 
in series. 



GALVANOMETERS 239 

Table XII. Tangent Galvanometer Constants. — Values of H 



Boston, 


0.699 


New Haven, 


0.731 


Chicago, 


0.759 


Philadelphia, 


0.783 


Denver, 


0.919 


Portland, Me., 


0.674 


Jacksonville, 


L094 


San Francisco, 


1.021 


London, 


0.745 


St. Louis, 


0.871 


Minneapolis, 


0.681 


Washington, 


0.810 


New York, 


0.744 







Since the tangent of the angle of deflection in Formula (80) 

■ . . H X r 

is always to be multipHed by a constant number, — — — , for a 

particular instrument and place, this number is called the con- 
stant of the galvanometer. 

H X r 
Let K = constant of the galvanometer = — — — , then from 

Equation (80), 

I = K X tan d (81). 

Problem 94. — A Daniell cell is connected to 4 coils of the student's 
tangent galvanometer connected in series, and the needle is deflected 30 
degrees. The diameter of the coil is 8 inches, and with 4 coUs in series 
having 2 turns per coil, the total turns are 8. What current is flowing 
through the instrument if it is located in New York? 

For New York H = 0.744; also r = 4 inches, N = 8 turns, tan 30° = 
0.5774. 

By Formula (80) 

H y r 744 x 4 

I = ^-^ X tan d = ^!il^^-A^ X 0.5774 = 0.214 ampere. 

N 8 

Problem 95. ~ What is the constant of the galvanometer in Problem 94. 

K= 5^^=^^*1^ = 0.372. 

N 8 

201. Thomson Galvanometer. — In the Thomson galva- 
nometer (Fig. 181) great sensibility has been attained by bring- 
ing the coil as close to the needle as possible and winding it 
with many turns of very fine wire. 

On the back of a small mirror, about | inch in diameter, are fastened by 
shellac, a number of magnetic needles with their N-poles in one direction. 
The mirror is suspended in the center of the coil, so that the needles hang 
horizontally, by a fine cocoon silk fiber which extends the entire length 
of the vertical brass tube shown in Fig. 181. The cylindrical box housing 



240 



LESSONS IN PRACTICAL ELECTRICITY 




Fig. 181.— Thom- 
son Mirror-reflecting 
Galvanometer (Sin- 
gle-coil Type.) 

position of the 
scale is located at 
the center so that 
the beam may 
swing to the right 
or left of zero. 
The spot of hght 
is brought to the 
zero position by 
the controlling 
magnet, or by 
twisting the fiber 
suspension by 
means of the 
knurled knob at 
the top of the 



the coil is mounted on a tripod, provided with level- 
ing screws, and can be rotated on its vertical axis. 
The curved controlling magnet, arranged on the 
vertical tube, can be revolved, or raised and 
lowered, with regard to the magnetic needle. The 
instrument is most sensitive when placed with its 
coil in the magnetic meridian, with the controlling 
magnet elevated to such a position that its force 
upon the suspended needles partly neutralizes the 
action of the earth's attractive force upon them. 

202. Reading Devices for Mirror-type 
Galvanometers. — To use the Thomson gal- 
vanometer (Fig. 181) or any other mirror- 
reflecting galvanometer, the room is dark- 
ened and a ray of light is projected upon 
the galvanometer mirror from a light source 
placed about two or three feet distant from 
the galvanometer. A graduated scale is 
fixed just above the source of light and the 
suspended system of the galvanometer is ad- 
justed so that the reflected beam of light 
strikes the scale. Fig. 182 shows a Leeds 
& Northrup reading device consisting of a 
galvanometer scale and lamp. The zero 




Fig. 182. — Reading Device for Use with Mirror- 
type Galvanometers. 



GALVANOMETERS 



241 



^^ 




Fig. 183. — Telescope and Scale 
for Use with Mirror-type Galvanom- 
eters. 



tube. The angle between the original and reflected beams of 
hght will be twice the angle of deflection of the mirror; the 
deflections of the spot of light on the scale are practically pro- 
portional to the strength of cur- 
rents through the instrument. 

Another reading device, shown 
in Fig. 183, does not require a 
dark room, as the scale read- 
ings are reflected in the mirror 
and their value observed by 
means of the telescope. 

203. Astatic and Differential 
Galvanometers. — If two needles 
of equal magnetic strength are 
fastened, one above the other, 
to a vertical rod with Hke poles in opposite directions, thus 
forming an astatic needle, and the rod is suspended, the earth's 
field has almost no directive force on the 
magnetic system. This principle is used in 
increasing the sensibility of galvanometers. 
The Thomson mirror-reflecting astatic 
galvanometer has a coil surrounding each 
of the needles forming the astatic needle, 
and these coils are connected so that the 
direction of current in both coils will tend 
to turn the system in the same direction. 

In this type of instrument the magnetic needles 
are compound and fastened to a small mica disk; 
the construction of the movable system in this in- 
strument is shown in Fig. 184. Two mica disks, to 
which the needles are secured, are joined by a stiff 
wire, the mirror being mounted on a mica vane 
and secured to this wire. The mica vane assists in 
damping, by increasing the air resistance to turn- 
ing, thus preventing the system from swinging 
back and forth for a long time after each deflection, 
and renders the instrument dead-heat. The whole system is suspended by 
a cocoon fiber attached to the upper end of a vertical brass tube, mounted 
on top of the case containing the coils A and B. A controUing magnet 
N S, is also provided to bring the needle system to zero and to alter its 
sensibiHty. The coils A and B may be used separately for comparing two 




Fig. 184. — Mirror- 
reflecting Astatic Gal- 
vanometer. 



242 



LESSONS IN PRACTICAL ELECTRICITY 



different current strengths at the same time by having the direction of 
the current in the coils such as to tend to turn the moving system in oppo- 
site directions. When so used the instrument is called a differential gal- 
vanometer. 

204. D'Arsonval Galvanometer. — The D'Arsonval galva- 
nometer (Fig. 185) is an example of that class in which the mag- 
net is stationary and the mov- 
able system consists of a small 
coil of wire instead of a mag- 
netic needle. The coil of wire 
is wound upon a rectangular 
bobbin and suspended by a fine 
silver or phosphor bronze wire 
between the poles of a laminated 
horseshoe magnet, so that the 
horizontal axis of the coil is at 
right angles to the magnetic lines 
of force between the poles of 
the magnet. When a current 
is led to and from the coil by 
means of the suspension wires 
above and below it, the coil 
becomes a magnetic body, and 
tends to turn so that its lines 
of force will be in the same direc- 
tion as those of the permanent 
magnet. The coil will move 
to the right or left, depending upon the direction of current 
through it. This tendency to rotate is opposed by the torsion 
of the suspension wire, and the motion continues until the 
turning effort (or torque) due to the current is equal to the 
opposing torque of the suspension. 

A stationary piece of soft iron is arranged in the center of 
the coil and supported from the back, its purpose being to 
increase the strength of the magnetic field in which the coil 
moves by reducing the reluctance of the flux path. By properly 
shaping the pole pieces the magnetic field may be modified 
so that the deflection of the coil will be directly proportional to 
the current traversing it. 




Fig. 1&5. — D'Arsonval Galva- 
nometer. 



GALVANOMETERS 



243 



If the coil is wound upon a non-magnetic metallic frame, the 
instrument will be very dead-beat, for the instant the coil 
moves induced currents are set up in the coil frame, and these 
are in such a direction as to tend to stop its movement ( Ij 254) . 
A mirror is attached to the coil so that the instrument may 
be used with a telescope and scale (Fig. 183) or with a lamp and 
scale (Fig. 182). 

To ascertain the torque on the moving system of a D'Arsonval galva- 
nometer, let 

I = current in amperes, 
A =* area included by the coil, 
N = number of turns in the coil, 
H = field intensity in the air gap where coil is located. 

' torque =AxNxIxH. 

This equation shows that a sensitive instrument should have a strong 
magnetic field, and that the coil should have many turns of wire wound 
on a relatively large bobbin. 

• These principles are utiHzed in the high-sensibihty D'Arson- 
val galvanometer shown in Fig. 186, 
in which the magnets are of large sec- 
tion in order to secure an intense field. 
The coil is suspended between the 
specially shaped pole pieces and has 
a resistance of about 500 ohms. One 
volt will produce a deflection of 1 mm. 
division at a scale distance of 1 meter 
(from mirror) through a resistance of 
10,000 megohms. 

A portable form of D'Arsonval gal- 
vanometer that is quite sensitive and 
particularly well adapted for the meas- 
urement of very small currents, for 
measuring insulation resistance and 
for Wheatstone bridge resistance meas- 
urements (^232) is shown in Fig. 187. 

In this particular form the moving coil, bility*" D'Arsonsa!" oSva- 
instead of being supported by a deh- nometer with Protecting 
cate suspension wire, is accurately Case Removed, 
fitted into jeweled bearings. The movement of the coil is 




Fig. 186. — High Sensi- 



244 



LESSONS IN PRACTICAL ELECTRICITY 



controlled by means of two springs which act against each 
other; this method is more certain in 
action than the torsion of a long sus- 
pension wire, and less liable to injury. 
This principle is used in the construc- 
tion of the Weston instruments (T[212) 
for measuring direct currents. 

The advantage of the D'Arsonval 
type of instrument over that of the 
Thomson form is, that it is not affected 
by the earth's or other external mag- 
netic fields, so that it may be used in 
close proximity to dynamos. 

205. The Ballistic Galvanometer. — 
A form of D'Arsonval galvanometer 
which is used for measuring momen- 
tary currents (as induction currents or 
condenser discharges (H 347)) is called 
a ballistic galvanometer (Fig. 188). Its 
coil is wide, is constructed to have con- 
siderable weight, and is arranged to have 

a small damping effect. If a momentary current be passed 




Fig. 187. — D'Arsonval 
Gah^anometer. 

Made by the Weston Elec- 
trical Instrument Co. 




Fig. 188. — • Ballistic Galvanometer with Attached 

Scale and Telescope. 

Made by the Leeds & Northrup Co. 

through its coils, the impulse given to the element does not 
cause appreciable movement of the magnetic system until the 



GALVANOMETERS 



245 



Oafvanomefer 



current ceases, owing to the inertia of the heavy moving parts, 
the result being a slow swing of the system. The maximum 
deflection or ''throw" is noted on the scale just at the point 
where the system ceases to move and begins to swing back to 
zero. This throw is a measure of the quantity of electricity 
sent through the coils. The instrument shown has a resis- 
tance of about 2000 ohms and will produce a deflection of 1 mm. 
on the scale by a quantity of electricity of about 0.003 micro- 
coulomb, the time of the ballistic throw from the position of 
rest to its maximum deflection being nearly 5 seconds. 

206. Ayrton Shunt. — A shunt which is extensively used with 
galvanometers is arranged as in Fig. 189; its external appear- 
ance is shown in Fig. 177. It 
may be used with galvanometers 
having widely different resis- 
tances. It will be observed that 
the galvanometer in Fig. 189 is 
shunted by the entire shunt com- 
posed of four resistances a, b, c 
and d in series, when the switch 
arm is placed on the contact 
marked 1. Let the current that 
flows through the galvanometer 
for this position of the switch 
arm be I. The resistances a, b, 
c and d of the shunt are so cal- 
culated that when the arm is 
on contact 0.1 the galvanometer current is 0.1 I, when on 
contact 0.01 the galvanometer current is 0.01 I, and when on 
contact 0.001 the galvanometer current is 0.001 I. Note in Fig. 
189, when the contact arm is moved from right to left, that 
resistance is cut out of the shunt and added to the galvanom- 
eter circuit. Consideration will show that if R be the entire 
resistance of the shunt then 




Fig. 189. 



Diagram ot Ayrton 
Shunt. 



— R, c = — R 
10 ' 100 



d, and b = 



999 

looo 



R - c - d, 



Thus, if R= 3000 ohms, then d = 2700 ohms, c = 270 ohms, 
b = 27 ohms and a = 3 ohms. 



246 LESSONS IN PRACTICAL ELECTRICITY 



QUESTIONS 

1. State how you would proceed to measure the current flowing through 
a number of incandescent lamps with a high-resistance galvanometer. 

2. The sensibility of a certain galvanometer is four megohms. What 
is meant by this statement? 

3. Give a general classification of galvanometers according to the 
principles employed in their construction. 

4. Upon what factors does the sensibility of a tangent galvanometer 
depend? 

5. Why is it necessary to construct such very sensitive instruments? 

6. What advantage does a dead-beat galvanometer possess over one 
that is not so constructed? 

7. Explain what is meant by a differential and a ballistic galvanometer. 

8. How would you arrange a low-resistance sensitive galvanometer so 
that it could be used for measuring electrical pressure? 

9. Explain how a galvanometer can measure electrical pressure, since 
the deflection of its magnetic system is dependent upon the strength of the 
current actuating it. 

10. What are the advantages of a D'Arsonval galvanometer over the 
tangent type? 

11. How would you construct a sensitive D'Arsonval galvanometer? 

12. Make a sketch of a double coil astatic galvanometer with the coils 
joined in parallel. Show the direction of current around the needle, and 
indicate the direction in which the system will be deflected by the current. 



PROBLEMS 

1. An unknown current deflects the needle of a tangent galvanometer 
27 degrees; the galvanometer constant is 0.65. What is the strength of 
current flowing through the instrument? Ans. 0.33 ampere. 

2. A current of 4.6 amperes is sent through the galvanometer of Prob- 
lem 1. What will be the corresponding deflection of the needle? Ans. 82°. 

3. The resistance of a galvanometer shunt is 0.2 ohm and that of the 
instrument with its leads 24 ohms. What pressure is required to send 10 
amperes through the joint resistance of the galvanometei and its shunt in 
parallel? Ans. 1.9 volts. 

4. How much of the current flows through the galvanometer in Prob- 
lem 3? Ans. 0.082 ampere. 

5. What is the multiplying power of the above shunt? Ans. 121. 

6. A four-coil Ayr ton shunt having the ratios depicted in Fig. 189 
has a total resistance of 10,000 ohms. Calculate the resistanca of each coil. 



LESSON XVII 

AMMETERS AND VOLTMETERS 

Ammeters or Ampere-Meters — Solenoidal Ammeter, Gravity Type — 
Thomson Inclined-Coil Ammeter — Weston A.C. Ammeters — Hot- 
Wire Ammeters — Weston D. C. Ammeters — Ammeter Shunts — 
Portable Dynamometer Ammeter; Electrodynamometer — Connect- 
ing Ammeters in Circuit — Measurement of E. M. F. and Potential 
Difference — Construction of Voltmeters — Weston Direct-Current 
Voltmeters — Multipliers — Connecting Voltmeters — Potentiometer 
— Questions. 

207. Ammeters or Ampere-Meters. — An ammeter, which 
is the commercial name for ampere-meter, is a galvanometer 
so constructed that the deflection of the needle indicates 
directly the strength of current in amperes flowing in a circuit 
in which it may be inserted. A great variety of measuring in- 
struments have been developed, based upon the principles given 
in TfTf 20 and 192. The instruments in general use are classi- 
fied according to their construction into two types: (1) fixed 
coil and moving iron type, and (2) fixed permanent magnet 
and movable coil type. 

Instruments of the moving iron type may be used to measure 
either direct or alternating current, but those of the perma- 
nent magnet and movable coil type can only be used to meas- 
ure direct current. 

A good ammeter should have a very low resistance, so that 
very little of the energy of the circuit in which it is inserted 
will be absorbed by it; the needle should be dead-beat, and so 
sensitive as to respond to minute variations of current; the 
scale divisions should not be cramped at the scale ends, but even 
throughout; and the accuracy of the instrument should not 
be impaired when in close proximity to powerful magnetic 
fields, as surround switchboard conductors or dynamos. Amme- 
ters are divided according to their use, into two classes: (1) a 

247 



248 



LESSONS IN PRACTICAL ELECTRICITY 




190. — Solenoid Gravity 
Ammeter. 



portable type, generally of a high class of construction and 
accuracy, used for measurements of precision, and (2) the 
switchboard type, in the construction of which such refinement 
of precision is not required. In some meters of both types the 
whole current passes through the ammeter, while in others the 

ammeter is shunted (^ 199). Mil- 
liammeters are ammeters in which 
the scale is graduated to read di- 
rectly in thousandths of an ampere. 
208. Solenoidal Ammeter, Gravity 
T3rpe. — In this simple type of am- 
meter, the magnetizing current 
causes the attraction of a piece of 
suspended iron. The current passes 
around a helix of heavy wire, which 
is bent in the arc of a circle, C in 
Fig. 190. A soft iron core A, bent to the same arc, is suspended 
at P so that one end is free to be sucked up into the helix, C, 
by the field of the magnetizing current. A pointer attached 
to the movable iron core 
moves over the scale, which 
is calibrated by sending 
known currents through the 
helix. The control is effected 
by means of the weight W, 
called a gravity control. 
Suppose that 10 amperes are 
sent through the helix, and 
the core moves to such a 
position as to accommodate 
through itself the greatest 
number of the magnetic lines 
of the helix, then the limit of 
the scale is attained and the 

range of the instrument is from to 10 amperes. The objec- 
tion to this type of instrument is that the movement of the 
core is much greater at some positions than at others for the 
same increment of current, giving a scale of unequal divisions, 
and generally cramped at each end. The instrument is not 




Fig. 191. 



Thomson Inclined-coil 
Ammeter. 



AMMETERS AND VOLTMETERS 



249 



dead-beat, is readily affected by outside magnetic fields, and 
can only be used in a vertical position. This type of instru- 
ment may be calibrated for use on alternating-current circuits 
as well as for direct-current circuits. 




Fig. 192. — Construction of Inclined-coil Ammeter. 

209. Thomson Inclined-Coil Ammeter. ^ The Thomson 
ammeter, constructed in the portable and switchboard patterns, 
is another form of the solenoidal 
type instrument, having a fixed 
coil and movable magnetic vane. 
The movable element consists of 
a small piece of iron so placed 
that it will gradually move to a 
position to accommodate 
through itself the greatest num- 
ber of fines of force of the mag- 
netizing coil. A view of the 
portable type, with cover re- 
moved, is shown in Fig. 191, 
and a sectional view in Fig. 192. 
A circular coil of wire, C, is 
mounted with its axis inclined 
to the horizontal. Through the 
center of the coil is passed a 
vertical shaft mounted between 
jewel centers and carrying a pointer at its upper end. A small 
iron vane, A, is suitably attached to the shaft at an angle, 




Fig. 193. — Interior View of 
Weston A. C. Ammeter. 



250 



LESSONS IN PRACTICAL ELECTRICITY 



and the movable system is controlled by the two flat springs 
S, S. When current is passed through the coil the vane tends to 
turn against the action of the springs, so as to become parallel 
to the lines of force passing downwardly through the center 
of the coil. The turning of the shaft causes the pointer P 
to sweep over the scale. The coils for large sizes of instru- 
ments are generally wound with a few turns of flat insulated 
copper ribbon having a very low resistance. These meters 
are adapted for use with alternating or direct currents. 

210. Weston A. C. Ammeters. — The instruments made by 
the Weston Electrical Instrument Co. primarily for measur- 
ing alternating currents 
and alternating E. M. 
F.'s are also of the 
''moving iron" type but 
are so constructed that 
many of the defects of 
the other solenoidal 
types have been elimi- 
nated . The moving ele- 
ment consists of a small 
curved piece of iron 
fastened to a light 
pivoted shaft (Fig. 193). 
To this shaft is also 
fastened a truss form 
of pointer made of thin 
aluminum tubing, to which is attached a balance cross and a 
small vane. Near the movable element and concentric with 
it is a small curved tongue of soft iron, which is rigidly held 
by a suitable support. Surrounding this is a field coil, made 
up either of a large number of turns of fine wire when the 
instrument is to be used as a voltmeter, or else of one or more 
turns of heavy wire when designed as an ammeter. When a 
current is passed through the field coil, the movable element 
and the fixed tongue of iron become magnetized by induc- 
tion; since both pieces of iron are within the field coil, their 
adjacent ends will have like polarities and consequently there 
win be repulsion between them. The only motion possible is 




Fig. 194. 



External View of Weston A. C. 
Ammeter. 



AMMETERS AND VOLTMETERS 



251 



the rotation of the movable element; this motion is opposed, 
and therefore controlled, by the action of a delicate spiral 
spring. The fixed tongue has a triangular shape so that the 
scale becomes more uniform. Damping of the movable system 
is caused by the vane which moves through confined air in 
the fan-shaped pocket, shown in Fig. 193 with its cover re- 
moved. An external view of this type of instrument is shown 
in Fig. 194. 

211. Hot- Wire Ammeters. — The hot-wire type of ammeter 
utilizes the heating effect of the electric current for measuring 
current; the flow of current through a wire causes heating and 
a consequent expansion of the 
wire through which it passes. 
The expansion of the wire is 
taken up by a spring which 
causes a pointer to move 
across a graduated scale. 

Instruments of this type 
are not affected by magnetic 
fields and may be used to 
measure either direct or al- 
ternating currents, but there 
are certain objections to their 
use, namely: they are slow in 
action, require frequent re- 
setting to zero and consume a greater amount of energy than 
other types. However, this type is particularly well adapted 
to measuring alternating currents of high frequency as used in 
wireless telegraphy, owing to the fact that the self-induction 
(^257) of the wire is practically zero. 

Fig. 195 shows the mechanism of a hot-wire ammeter. The 
wire CD passes around the pulley K and is held taut by 
spring S acting on the insulating plate B. The current to be 
measured flows only through the branch C of the wire, and 
consequently that branch lengthens. The slack is taken up by 
a shght rotation of the pulley K, which causes arm A (pivoted 
at -K) to move. This arm has two prongs at its lower end 
between which a thread is stretched after looping itself around 
shaft T at the lower end of the pointer P. The slight expan- 




Fig. 195. — Hot-wire Ammeter. 



252 



LESSONS IN PRACTICAL ELECTRICITY 




Fk. 196. 



sion of the wire is thus magnified by the mechanism so that 
a large scale reading is obtained. 

212. Weston D. C. Ammeters. — The instruments, manufac- 
tured by the Weston Electrical Instrument Co., for measuring 

direct currents and electromotive 
forces, are in reality a portable form 
of D'Arsonval galvanometer, having 
a permanent magnet and a movable 
coil. When the instrument is designed 
as an ammeter the movable coil is 
shunted across a low resistance 
(V 213), if it is to be used as a volt- 
meter (If 217) a high resistance is in- 
serted in series with the movable coil. 
This type of instrument is far superior 
to the '^ moving iron" type; it is ex- 

•^ - f ^u Aur^^^^^l'r^ T " tremely accurate, has a uniform scale, 
cmt of the Weston D.C. In- i • , i . i i i ^ . * 

struments. and IS absolutely dead-beat. A per- 

manent horseshoe magnet M is fitted 
with soft-iron pole pieces P, P (Fig. 196) between which a 
stationary cylinder of soft iron C is supported by a brass plate 
extending across the pole 
pieces. The iron cylinder is 
smaller in diameter than the 
bore of the pole pieces, so that 
the magnetic lines of force pass 
across this air gap, making a 
very strong and uniform mag- 
netic field. 

The movable coil (Fig. 197) 
consists essentially of a light 
rectangular coil of copper wire, 
usually wound upon an alumi- 
num frame, pivoted in jewel 
bearings, and mounted to 
rotate in the annular space 
between the soft iron core and 
the specially formed pole pieces of the permanent magnet (Fig. 
198). A hght tubular pointer is rigidly attached to the coil and 




Fig. 197. — Movable Coil, 
and Pointer of Weston D.C. 
ments. 



Springs 
Instru- 



AMMETERS AND VOLTMETERS 



253 



moves over a graduated scale. The terminals of the coil are 
connected to the horizontal spiral springs, against which the coil 
acts when it tends to rotate, the springs serving also to con- 
duct the current to and from the coil. When a current is 
sent through it, the coil tends to move .through the mag- 
netic field, to take up a position so that its lines of force 
will be in the same direction as those of the field. It will so 




Fig. 198. 



Method of Mounting Movable Coil in 
Weston Instruments. 



move until the torsion of the springs is balanced by the force 
tending to move the coil, when the pointer will indicate the 
angle of deflection. The angle of deflection is nearly propor- 
tional to the current throughout the movement, which results 
in a very uniform scale. The movable coil is extremely light, 
the friction small, and hence the instrument is very sensitive 
to minute variations of current. The instrument is carefully 
balanced, so that it may be used in a horizontal or vertical 
position. An ammeter, however, should always be calibrated 
in the position in which it is to be used. 



254 



LESSONS IN PRACTICAL ELECTRICITY 




Fig. 199. — Weston Ammeter with 
Self-contained Shunt. 



The aluminum frame on which the coil is wound has an elec- 
tromotive force induced in it, when rotating in the magnetic 
field, which causes eddy currents ( % 254) to flow around the 
frame in the opposite direction to the current in the coil. 
These momentary currents tend to stop the motion of the 

coil, and have the effect of 
preventing the needle from 
oscillating, thus bringing it to 
rest quickly at the proper 
position and making the in- 
strument very dead-beat. 

A mirror is located just 
below the scale of the port- 
able instruments. By looking 
down on the pointer so that it 
is directly over its reflection 
in the mirror, errors in read- 
ing the scale divisions due 
to parallax ^ are avoided. In 
D. C. instruments the post marked + is the one at which the 
current should enter the instrument so that the coil will be 
deflected in the right direction. A Weston portable Model 1 
p. C. ammeter with self-contained shunt is shown in Fig. 199. 
213. Ammeter Shunts. — As the Weston direct-current in- 
struments are merely D'Arsonval galvanometers, they may be 
used either as ammeters or voltmeters according to the resis- 
tance of the movable coil, that is, whether the resistance is 
low or high. These instruments are really all millivoltmeters 
a few thousandths of a volt being sufficient to cause a full- 
scale deflection of the needle, and, as the wire on the movable 
coil is so fine that it can carry but a small fraction of an ampere, 
a shunt (H 199) must be placed across the movable coil in 
order to use this device to indicate larger currents. Only a 
small fraction of the main current will then flow through the 
moving coil, the remainder passing through the shunt. 

The shunt is made of such a material or combination of 
materials, forming a special resistance alloy, that does not appre- 

/ The apparent angular displacement of an object when seen from two 
different points of view. 



AMMETERS AND VOLTMETERS 



255 




Fig. 200. — Portable Ammeter 
Shunt. 



ciably change in resistance as its temperature changes. The 
shunt may be placed in the instrument, in a separate port- 
able case (Fig. 200) , or in the busbars on the back of a switch- 
board. Fig. 201 shows a shunt used with the switchboard type 
of instruments. The lead wires to the shunt, the instrument, 
and the shunt are all numbered 
to correspond, so that when used 
together the indications agree 
with the calibration. The shunt 
leads should never be shortened, 
because the decreased resistance 
in the shunt circuit would permit 
more current to flow through it, 
so that the indicated readings 
would be higher than the actual 
current flowing. One advantage 
of an external shunt in switch- 
board instruments for power sta- 
tions is,' that instead of running heavy copper cables to a dis- 
tant ammeter, a shunt may be inserted in the cable circuit and 
the two small-sized shunt leads wired to the instrument, thus 
effecting an economy in copper and construction. The resis- 
tance of the instrument and its shunt is very low; little energy 

will, therefore, be lost when 
it remains continually in 
circuit, 

A number of shunts are 
sometimes furnished for a 
single portable instrimient 
and mounted in a separate 
case called a shunt box, 
which is used for increasing 
the range or capacity of the instrument. For example, suppose 
the coil with a shunt of 0.004 ohm receives sufficient current to 
deflect the pointer entirely across the scale, and this deflection 
corresponds to 50 amperes in the main circuit. The difference 
in pressure between the shunt terminals is practically equal to 
I X R = 50 X 0.004 = 0.2 volt. With a shunt of half the former 
resistance or 0.002 ohm, the pressure applied to the movable 




Fig. 201. — Separate Shunt for Switch 
board Ammeters. 



256 LESSONS IN PRACTICAL ELECTRICITY 

coil for the same current will be equal to I x R = 50 x 0.002 
= 0.1 volt, or the coil will receive only one half the former 
current, and thus be deflected only to the middle of the scale. 
The range of the ammeter is now to 100 amperes, or each 
scale reading must be multiplied by 2 to obtain the true value 
of the current when used with this shunt. In the same manner 
with a reduction of the resistance of the shunt to one-tenth 
of its original value, the range of the instrument is increased 
tenfold and the readings are multiplied by 10. 

To determine the resistance of a shunt for measuring cur- 
rents larger than the capacity" of an ammeter, let 

R = resistance of shunt required, 
r = resistance of ammeter, 
A = range of ammeter, 
Ai = desired range of ammeter. 

Then 

R=-^— xr (82). 

The indicated readings obtained must be multiplied by — to be 

A. 

correct. 

Problem 96. — (1) What will be the resistance of a shunt required to 
increase the capacity of an ammeter from 150 to 600 amperes? Resis- 
tance of the instrument is 0.009. (2) What will be the multiplying power 
of the shunt? 

By Formula (82) 

A 1 ^0 

R = — ^ X r = — -"^r^X 0.009 = 0.003 ohm. 
Ai - A 600 - 150 

Multiplying power of the shunt = j^ = —r^ = 4. Likewise by Formula (76) 

G , 0.009 , , 

^ = s-^'=aoo3 + ' = '- 

214. Portable Dynamometer Ammeter-Electrodynamometer. 

■ — The dynamometer ammeter is an instrument for measuring 
current strength by the reaction between two coils, one of 
which is fixed and the other movable, and through which the 
current to be measured is passed. The operation and prin- 



AMMETERS AND VOLTMETERS 



257 



IS 




ciples involved are substantially the same as those used in 

the eledrodynamometer, herein described, but the scale 

graduated directly in amperes. 

The general appearance of a Sie- 
mens dynamometer is illustrated 

in Fig. 202, and the diagram of 

the circuits is shown in Fig. 203. 

The fixed coil CD, containing a 

number of turns of wire, is 

fastened to a vertical support. 

The movable coil AB of a very 

few turns of wire, is large enough 

to embrace the fixed coil when 

their planes are at right angles 

to each other, and is suspended 

by a strong piece of thread below 

the celluloid dial. The ends of 

this coil, being free to move, dip 

into two cups of mercury, located 

one above the other along the 

axis of the coil. Connections are 

made as indicated, so that the two coils 
are in series when connected to an ex- 
ternal circuit. The planes of the coils 
should be at right angles to each 
other. When the current flows through 
both coils, the movable coil tends to 
turn, according to Law 2 (Lesson XV) 
for currents flowing parallel to each 
other. 

The force measured is the force which 
must be applied to keep the movable 
coil at right angles to the other against 
the turning effort due to the current. 
One end of a spring is rigidly fastened 
to the movable coil, and the other end 
terminates in a mill-headed screw on 
the face of the dial, which can be turned 
so as to apply torsion to the spring. The movable coil carries 



Fig. 202. 



— Siemens Dyna- 
mometer. 



Poinfen 




Fig. 203. — Connections 
of Siemens Dynamometer. 



258 LESSONS IN PRACTICAL ELECTRICITY 

an upwardly-extending pointer which swings between two 
stop pins on the dial and points directly to a fixed zero line 
when the coils are at right angles. To the torsion screw is 
attached a pointer which sweeps over a degree scale. When 
the movable coil is deflected against a stop pin, the torsion 
screw is rotated in a direction to oppose the current's action, 
and when the coil is brought back to its original position the 
number of degrees through which the torsion pointer was 
turned, is noted. 

The current is directly proportional to the square root of 
the angle of torsion. For example, if with one current the 
number of degrees noted was 36 and with another current 144, 
then the currents are to each other as the square roots of 36 
and 144, or as 6 is to 12, or one current is twice as strong as the 
other. To determine the current in amperes, the square root 
of the angle of torsion is multiplied by a constant found by 
caHbration and furnished by the makers. The fixed coil is 
usually divided into two coils wound with a different number 
of turns, either of which is inserted in series with the movable 
coil, and the terminals are brought out to separate posts. Thus 
in measuring a current known to be between, say, one-tenth 
and 1 ampere, a certain pair of binding posts is used, and if 
between 1 and 100 amperes, the other pair of posts is used. 
This arrangement produces a double-scale instrument whereby 
both small and large currents can be measured with accuracy. 
The Siemens dynamometer is an accurate instrument con- 
nected in circuit like an ammeter and has the advantage of 
being adapted for use with either direct or alternating currents. 
When used on a direct-current circuit more accurate results 

are obtained by taking the 
Ca m^ average value of two read- 
ings made with the current 
Genenrtor 6 6 t)i-c^mps Aowing in opposite direc= 

tions. 
215. Connecting Am- 
Fig. 204 — Method of Connecting an meters in Circuit. — Since 

Ammeter m a Circuit. -i , - i x x i 

the total current to be meas- 
ured in any circuit must flow through an ammeter, an am- 
meter must always he connected in series with the circuit and 




AMMETERS AND VOLTMETERS 



259 



between the generator and apparatus receiving current, as in 
Fig. 204". Suppose an ammeter whose resistance is 0.1 ohm is 
incorrectly placed in parallel with some incandescent lamps con- 
nected to a generator. The current that would flow through 
the ammeter if the pressure is 110 volts between the mains 

rp 1 1 n 

would be, by Ohm's Law, I = — = — — = 1100 amperes, or 

K. 0.1 

enough to totally destroy the instrument by excessive heating, 
since the current-carrying 
capacity of the wire within 
the ammeter would be far 
below this value. 

When a separate or ex- 
ternal shuiit is used with 
an ammeter the shunt is 
inserted in series with the 



■Generator 




Lamps 




Shunt 

Fig. 205. — Connection of an Ammeter 
with External Shunt. 



T 



circuit and the instrument connected across the shunt by the 
small-sized lead wire furnished for the purpose (see Fig. 205). 

216. Measurement of E. M. F. and Potential Difference. — 
Consider first the following hydraulic analogy in which it is 
desired to measure the true water pressure at the point C in a 
_ pipe, Fig. 206, through 

which a current of water 
is flowing from A to B. 
Instead of using a spring 
gauge, which consumes 
no water in making the 
measurement, we will 
use a turbine wheel at 
point C . A j et of water 
from tank T forced 
against the wheel, which revolves at a particular speed for a 
given pressure at point C, say 1600 revolutions per minute, 
corresponding to a pressure of 50 pounds per square inch at C. 
7s this the accurate "pressure at point C, that is, the pressure that 
would he recorded by a spring gauge if inserted at point C f No. 
The turbine in measuring the pressure will increase the flow 
of water at point C, as some water must necessarily discharge 



Turbine 



"lijlj 

Fig. 206. — Measurement of Hydraulic 
Pressure. 



260 LESSONS IN PRACTICAL ELECTRICITY 

through it. The accurate pressure will not be recorded, but 
a lower pressure will be noted than that which would exist 
were the turbine not connected. The increased current of 
water through the pipe from A to C, due to the turbine outlet, 
causes a greater loss in pressure. If the turbine were made 
exceptionally small and so sensitive that a very minute stream 
of water from the outlet would actuate it, it would more nearly 
record the true pressure at point C, since very little more 
current would then flow than when it was disconnected. This 
turbine pressure meter must, therefore, be constructed so that 
only a very small amount of water will be used by it in measur- 
ing the water pressure. 

To measure the electrical difference of potential between two 
points requires a galvanometer constructed with a very high 
resistance, so that only a very minute current will flow through 
it, at the same time the current must be of sufficient strength 
to actuate the movable system, which is generally quite sensi- 
tive. To measure electrical pressure some current must,' there- 
fore, he used, and the true pressure will be greater than the indi- 
cated pressure by an amount equal to the volts lost on the line and 
generator which are required to transmit the voltmeter current to 
the instrument. The less this current the more accurate the indi- 
cation; consequently the best voltmeters have a very high resistance 
and their current is practically negligible. When a voltmeter is 
placed in parallel with any part of a circuit the resistance of 
the circuit is practically the same as before, since the volt- 
meter resistance is so very high; the current in the circuit is 
hot materially changed, and the calibrated indication records 
not the current in the circuit, or the current through the volt- 
meter, but the difference in pressure between the voltmeter 
terminals. The movement of its magnetic system, of course, 
depends upon the current flowing through the voltmeter, but 
the scale is calibrated by applying known E. M. F.'s to its 
terminals and marking the position of the needle with refer- 
ence to the scale for each particular pressure applied. In an 
ammeter the whole current passes through the instrument, or 
its shunt, and the instrument measures the current. A volt-^ 
meter measures the current flowing through it, but the cali- 
bration is in terms of the pressure causing this current to flow. 



AMMETERS AND VOLTMETERS 



261 




217. Construction of Voltmeters. — The same principles em- 
ployed in the construction of ammeters (^207 etc.) are em- 
ployed in constructing voltmeters, the only difference being 
that the windings are of very fine wire, suitable to the small 
current that is to be carried, and that extra resistance coils 
are generally added in series with the voltmeter coils to pro- 
duce an instrument of very high resistance, for the reasons 
already given. 

218. Weston Direct-Current Voltmeters. — The same me- 
chanical construction is employed in the Weston D. C. volt- 
meter as in this make of ammeter (1j 212), 
except that resistance is connected in series 
with the movable coil. A double-range 
Weston Model 280 miniature voltmeter is 
shown in Fig. 207, suitable for use with 
pressures as high as 150 volts, and its in- 
ternal connections are shown in Fig. 208. 
The 150- volt coil terminates in the two 
right-hand binding posts, and the current 
enters by the right-hand post marked +. 
A push-button in the lower corner serves 
to close the circuit. The resistance of the 

150-volt coil is about 11,000 ohms, and 

there are 30 divisions on the scale, or one 
division per 5 volts. The 3-volt coil ter- 
minates in the right-hand and left-hand 
posts, and has a resistance of about 220 
ohms. There are ten divisions on this 
scale per volt, or one-tenth volt per divi- 
sion. The double-range Weston stan- 
dard portable voltmeter. Model 1 (Fig. 
209), is a higher grade instrument than 
Model 280, and with it greater accuracy 
in voltage measurement may be had, 
since its internal resistance is higher and 
the scale is of greater length permitting a greater number of 
divisions for the full-scale length; a Model 1 voltmeter with 
a range of 150 volts would have a scale of 150 divisions or 
one division per volt, instead of 5 volts, as in Model 280. 



Fig. 207. — Weston 
Double-range Model 
280 Voltmeter. 




'Resistances-^ 




Fig. 208. Connec- 
tions of Double-range 
Voltmeter. 



262 



LESSONS IN PRACTICAL ELECTRICITY 



In using a double-range voltmeter, if in doubt about the value 
of the voltage to be measured, always use the higher-reading 
scale first, then if the value is below the limit of the low-reading 

scale, the left-hand terminal 
may be readily changed to 
the other post. If 150 volts 
are directly applied to the 
low-reading or 3-volt posts, 
the instrument will be 
seriously damaged and 
probably the insulation de- 
stroyed by a larger current 
flowing through it than the 
windings will carry. For 
the same reason any volt- 
meter should not be sub- 
jected to a higher voltage 
than is indicated upon 




Fig. 209. — Model 1 Weston Voltmeter. 







its scale. 

Voltmeters are cahbrated by means of standard cells and 
are made up according to the range of the instrument desired, 
by means of the extra resis- 
tance to be added. In a 
millivoltmeter the scale is grad- 
uated to read in divisions 
representing one-thousandth 
part of a volt, or one milli- 
volt. The Weston direct- 
current ammeter without its 
shunt, may be used as a milli- 
voltmeter, and when a high 

resistance is placed in series a/t i r 

with the movable coil the ^^' ' ^ ^^ ^^^' 

same instrument may be calibrated as a direct-reading volt- 
meter. 

219. Multipliers. — The high resistance connected in series 
with the movable coil of the direct-current instrument when 
it is to be used as a voltmeter, is called a multiplier, and 
if the instrument is to be used at all times as a voltmeter of 




AMMETERS AND VOLTMETERS 263 

given range, this high resistance is placed inside the instru- 
ment case. 

The range of any voltmeter may be increased to any prac- 
tical limit by inserting a resistance in series with the volt- 
meter; commercial multipliers (Fig. 210) that are used for 
this purpose, consist of resistance coils placed in a portable 
case. Multipliers are usually constructed with the resistance 
coils adjusted for the voltmeter with which they are to be 
used, as the resistance coil inserted in series with it should be 
a multiple of the voltmeter resistance, and the reading of the 
voltmeter is then multiplied by a constant, such as 2, 5, 10, 
etc., in order to determine the voltage of the circuit. 

A multiplier is of considerable value, in that it does away 
with the necessity of having a number of voltmeters of differ- 
ent ranges. 

220. Connecting Voltmeters. — Voltmeters are connected 
directly across the line, the voltage of which is required, or in 



U^ 




Fig. 211. — Connection of a Voltmeter and an Am- 
meter to a Circuit. 

parallel with the conductor between the ends of which the 
potential difference is required. Figs. 101, 102, etc., illustrate 
the proper connection for measuring the potential in the dif- 
ferent parts of a circuit. A voltmeter is never connected in 
series with the line and an ammeter never across or in parallel 
with the line, but always in series with it (see Fig. 211), 
The following problems will illustrate the reason for each 
particular connection. 

Problem 97. — A 150-volt coil of a Weston voltmeter has a resistance 
of 15,000 ohms. What cm-rent will it receive when placed across a circuit 
of 100 volts P. D.? 

F* 100 
By Formula (27) I = i^ = t^^^ = 0.0066 ampere. 



264 LESSONS IN PRACTICAL ELECTRICITY 

Problem 98. — In Fig. 211 the generator D maintains 110 volts across 
the mains at the lamps L when 22 lamps are connected. Each lamp has a 
resistance of 220 ohms. What current will be indicated by the ammeter? 

■p 220 
By Formula (30) J. R. = — = 7— =10 ohms. 
•^ nq 22 

F 110 
By Formula (27) I = — = "jTr = H amperes. 

Problem 99. — Suppose the voltmeter in Problem 98 has a resistance of 
15,000 ohms and is incorrectly placed in series with the lamps. What 
current will the lamps receive, assuming the potential to be 110 volts? 
F 1 1 

By Formula (27) I = ^ = 15 000 + 10 ^ ^"^^^^ ampere. 

The lamps will not illuminate with this current since 10 amperes were 
required before. 

Problem 100. — Suppose the ammeter of Problem 98 has a resistance of 
. 1 ohm and is incorrectly connected across the circuit, like the voltmeter 
in Fig. 211, what current will it receive if the P. D. is 110 volts? 

By Formula (27) ^ = ^ = -prT= HOO amperes. 
ix 0.1 

Unless the ammeter had a current- carrying capacity of 1100 amperes it 
would be destroyed by the excessive heat caused by such a large current. 

221. Potentiometer. — The potentiometer is an instrument 
used for comparing voltages with that of a standard cell by. 
an arrangement of variable standardized resistances, a galva- 
nometer, and a source of 

ImtI'^ ^ constant potential, such as 

a storage battery. The 
potentiometers made by 
different manufacturers 
differ in electrical "and 
Oalvanor^n- ''^'"^^^"^^'^^ ^^'^ mechanical details, there- 

Fig. 212. -Connections of Potentiometer, ^o^^' ^o attempt will be 

made to describe indi- 
vidual instruments. The principles of the potentiometer of 
whatever make may be readily understood from a study of 
Fig. 212, which shows a simple form of potentiometer consisting 
of a fine German-silver wire, AB, stretched between binding 
posts on a wooden base provided with a scale. Current is 
passed through this wire in one direction, A to B, from several 




AMMETERS AND VOLTMETERS 265 

constant-current cells so that a constant P. D. will be main- 
tained between the ends of the wire AB. 

If this potential difference is known, the cell, the E. M. F. 
of v/hich is to be determined, is connected in series with a gal- 
vanometer, and then in shunt with the potentiometer wire, 
so that its current will be in opposition to the potentiometer 
current. When the drop in volts on the length of the poten- 
tiometer wire is equal and opposite to the cell's E. M. F. no 
current will flow through the galvanometer, and its needle will 
stand at the zero position. This point is determined by sUd- 
ing the mcfvable contact C along AB, till balance of the needle 
is obtained at zero. Then the E. M. F. of the cell bears the 
same relation to the P. D. between the ends of the poten- 
tiometer wire AB, as the distance included between the cell 
termiinals, AC, bears to the whole length of the potentiometer 
wdre, AB. 

Suppose the movable contact C touches the wire AB at a 
point where the volts drop along that wire is greater than the 
E. M. F. of the cell being measured, then, the greater E. M. F. 
of the upper cells will force a current in the reverse direction 
through the cell under test, since the two batteries are in parallel, 
and although not directly across each other the cell under test 
is across enough of the voltage of the other cells to have its 
E. M. F. overpowered. The cells are delivering current through 
two parallel paths, one from A to B through the potentiometer 
wire, and the other from A to C through the cell under test and 
galvanometer against the E. M. F. of that cell; the latter cur- 
rent causes the galvanometer to be deflected in a certain direc- 
tion. Now suppose the movable contact C is brought to rest 
on the wire at such a point that the volts drop from A to C 
is less than the E. M. F. of the cell; then, a current will flow 
out of the cell through the potentiometer wire from A to C and 
through the galvanometer, which is then deflected in the oppo- 
site direction. When the movable contact is brought to a point 
on AB that does not deflect the galvanometer, the volts drop 
from A to that point is exactly equal to the E. M. F. of the cell 
under test, hence no current can flow in either direction through 
that cell, the galvanometer needle standing at zero, and the 
potentiometer is said to be balanced. 



266 LESSONS IN PRACTICAL ELECTRICITY 

If the E. M. F. of a cell is known and used as a standard of 
E. M. F., the E. M. F. of any other cell may be determined 
from this standard. The standard cell is first connected in the 
galvanometer circuit to the potentiometer wire (Fig. 212) and 
the distance, AC divisions on the scale, noted when balance is 
attained. The cell of unknown E. M. F. is then substituted for 
the standard, being connected in opposition as before, and the 
distance, say AD, noted when balance is obtained. The follow- 
ing relation then exists when AC equals the length on potenti- 
ometer wire balanced by the standard cell, and AD equals the 
length balanced by the cell of unknown E. M. F. : 

E. M. F. of standard length AC 

E. M. F. of unknown length AD' 

or 

1 t:^ i^fT T? E. M. F. of standard x AD ,.., 

unknown E. M. F. = -— . . (83). 

AC 

The potentiometer wire scale may be graduated to read in 
volts instead of inches. Thus, a wire 36 inches long with 3 
volts P. D. across its ends would correspond to 12 inches per 
volt. When the potentiometer wire is graduated in volts, a volt- 
meter may be readily cahbrated or recalibrated, by substitut- 
ing it for the cell and galvanometer, and noting the deflections 
on the voltmeter scale due to different potential differences 
apphed by moving the flexible slider along the potentiometer 
wire. The potentiometer in connection with a standard low 
resistance affords an accurate method for calibrating ammeters. 

Problem 101. — In a potentiometer test a standard cell of 1.05 volts 

E. M. F. produced a balance when 12 inches of the potentiometer wire 

were included between its terminals. What are the E. M. F.'s of two other 

cells that were measured if the potentiometer readings to produce balance 

were respectively 8 and 20 inches? 

_ , ^ ^ E. M. F. of standard X AD 
By Formula (83) unknown E. M. F. = j^ — 

1.05 X 8 



12 



0.7 volt = E. M. F. of the first cell. 



1 O^ V Ti 

Also ^ ^^ = 1.75 volts = E. M. F. of the second ceU. 



AMMETERS AND VOLTMETERS 267 



QUESTIONS 

1. What is the advantage of an ammeter of the stationary permanent 
magnet and moving coil type over one constructed to actuate upon the 
solenoid and moving iron principle? 

2. What is the advantage of the stationary coil and moving iron tj^e 
of instrument over the other type? 

3. In a station shunt- type ammeter a pair of shunt leads are used which 
are the same length as those furnished with the instrument, but of a smaller 
size. How will this affect the meter's indications? 

4. An ammeter coil with its leads has a resistance of 50 ohms, and the 
shunt has a resistance of 0.1 ohm. If 20 amperes are flowing through the 
circuit to which the shunted ammeter is connected, what current does the 
ammeter coil receive? Ans. 0.04 ampere. 

5. It is desired to use an ammeter of only 50 amperes capacity in a 
circuit through which 150 amperes are flowing. How would you do this? 

6. How much resistance would you use if the instrument in Question 
5 had a resistance of 0.08 ohm? Make a sketch. Ans. 0.03 ohm. 

7. By what should the indications of the ammeter in Question 6 be 
multiphed in order to obtain the true reading? 

8. A Siemens dynamometer is connected in series with some incandes- 
cent lamps and the torsion head must be turned through 121° to bring 
the movable coil to the zero position. Some lamps are then turned off and 
the angle indicated by the torsion head is 81°. What is the strength of 
current in each case if the constant of the instrument is 2? Ans. 22 am- 
peres; 18 amperes. 

9. What is the advantage of a dynamometer ammeter over one con- 
structed upon the D'Arsonval principle? 

10. What is the essential requirement in order to measure E. M. F. 
accurately, and how is it fulfilled in voltmeter construction? 

11. Since the mechanical construction and the resistance of the movable 
coil of a Weston voltmeter and ammeter are both the same, what then 
is the essential difference in the instruments? 

12. Give a numerical example to illustrate the use of a multiplier in 
extending the range of a voltmeter. 

13. What is a potentiometer and for what is it used? 

14. In a potentiometer test, balance of the galvanometer needle is 
attained with a standard cell of 1.05 volts for 210 divisions. For another 
cell the balance is attained at 430 divisions. What is the E. M. F. of this 
cell? Give a complete sketch. 



LESSON XVIII 

WATTMETERS AND WATT-HOUR METERS 

Measurement of Power and Energy — Indicating Wattmeter — Thomson 
Watt-Horn- Meter — Sangamo Direct-Current Watt-Hour Meter 
— Reading the Watt-Hour Meter — Questions. 

222. Measurement of Power and Energy. — The electric 
power expended in a circuit is equal to the product of the 
voltage E, and the current I, or P = E x I, Formula (54). 
These factors may be determined by a voltmeter and amme- 
ter; and when the readings of the two instruments are multi- 
plied together the result will give the true power expended in 
the circuit, provided the circuit is carrying a direct current. 
If, however, the current is alternating in character, the prod- 
uct of the volts and amperes only will not give the true power 
( % 356) unless the apparatus connected to the circuit is non- 
inductive, such as incandescent lamps. The power in either 
an alternating- or direct-current circuit may be measured by 
a wattmeter, which automaticall}^ multiplies the volts and 
amperes together, and will indicate the instantaneous value 
of the true power in either kind of circuit, regardless of whether 
the resistance connected in the circuit is inductive or non- 
inductive. 

Meters for the measurement of electrical energy are called 
watt-hour meters, and these devices take care not only of the 
power taken by a load but also of the duration of that load. 
The energy suppHed to a circuit by If 142 is 

u n .o • energy = E x I X t, 

or by If 148 is t^ . , ^ 

^ " energy = P x t. 

If P is the power in watts and t is the time in hours, then the 
energy is expressed in watt-hours. 

223. Indicating Wattmeter. — The indicating wattmeter 
measures the instantaneous values of the power in any circuit 

268 



WATTMETERS AND WATT-HOUR METERS 269 



to which it is connected, the power in watts being directly read 
from the scale, and it is, therefore, called an indicating watt- 
meter. Most wattmeters are constructed on the principle of 
the Siemens dynamometer, and operate upon the same prin- 
ciples' as the dynamometer ammeter ( T[ 214) but the two coils 
are not connected in series. The stationary coil, or current 
coil, is connected in series with the line like an ammeter and 
is wound with a few 
turns of heavy copper 
wire having a low resis- 
tance. Themovable coil, 
or voltage coil, is wound 
with many turns of very 
fine wire and connected 
in series with a high re- 
sistance. The construc- 
tion of the Weston dyna- 
mometer wattmeter is 
shown in Fig. 213. The 
two field coils, AA, are 
wound with wire which 
will permit the entire 
current to flow through 
them without raising 
their temperature appre- 
ciably, the terminals of these coils being brought out to two 
large binding posts. The movable potential coil B, mounted 
and constructed similar to the coil shown in Fig. 197, consists 
of a number of turns of fine insulated copper or aluminum wire 
and connected in series with a high resistance R, the terminals 
being brought out to independent binding posts shown at 
the right. A push-button switch, S, is inserted in the voltage- 
coil circuit. The movable coil thus corresponds to the volt- 
meter and is connected to any circuit in the same manner as 
a voltmeter. 

The current in the voltage coil will vary as the potential 
difference between its terminals, and the current through the 
current coil will vary as the current in the circuit in which 
it is inserted. The force acting upon the movable coil depends 




Fig. 213. — Construction of Weston In- 
dicating Wattmeter and its Connection in 
a Circuit. 



270 



LESSONS IN PRACTICAL ELECTRICITY 



on the current through both coils, or directly upon the watts 
expended in them. The movable coil turns against the torsion 
of the springs CC, and its pointer P swings over a scale gradu- 
ated in watts. The instrument is, therefore, direct reading, 
as in the case of a voltmeter. Fig. 213 shows the proper con- 
nections of the instrument for measuring the watts consumed 
by the incandescent lamps. 

The Weston instrument requires no adjustment to secure 
a balance of the forces acting, and so momentary fluctuations 

are readily noted on the 
scale. This instrument 
can be used on any cir- 
cuit and is rated accord- 
ing to the carrying ca- 
pacity of the current coil 
and the potential to be 
applied across the voltage 
coil. For example, in a 
particular 1500-watt in- 
strument the maximum 
current is 10 amperes and 
the maximum voltage is 
150 volts. The capacity 
of the voltage coil can be 
increased to any desired 
range by the use of a 
multiplier. 

Fig. 214 shows the 

X.- ^. . -r. . , , T^r . ^r .. external view of a port- 

Fig. 214. - Portable Weston Wattmeter, ^^j^ ^^^^^^ ^j^^^^^_ 

dynamometer-type of . indicating wattmeter. The two largest 
binding posts connect with the series coils through the four 
posts at the right-hand upper corner which enable the two 
coils to be connected in series or parallel with each other by 
means of short connecting links. The three small rubber- 
covered binding posts are for the potential wires and are 
marked ±, 150 and 75, thus providing two voltage ranges. 

224. Thomson Watt-Hour Meter. — The consumption of 
electrical energy is paid for by the consumer at a fixed rate per 




WATTMETERS AND WATT-HOUR METERS 271 

kilowatt-hour (^ 148), therefore, it is necessary to have some 
form of meter that will measure the amount of electrical energy 
in watt-hours, or kilowatt-hours. Meters for measuring the 
amount of electrical energy are sometimes called integrating 
wattmeters, since they sum up the work done during succes- 
sive intervals, but are more properly termed watt-hour meters. 
The indicating wattmeter gives the instantaneous values of 
the watts expended in a circuit, just as a voltmeter indicates 
the momentary pressure in volts. To find the watt-hour con- 
sumption of electrical energy by such a wattmeter, it would 
be necessary to multiply the average of a number of readings 
taken during a given time, by that time, expressed in hours 
(^ 148). As the name implies, the readings of a watt-hour 
meter gives the total watt-hour consumption of energy, or it 
automatically multiplies the average of the instantaneous 
indications by the time. Its principle of operation is that of 
the Siemens dynamometer (^214) but the movable coil 
rotates. The method of producing this rotation may be dem- 
onstrated as follows: 

In Fig, 203 continuous rotation of the coil AB around the coil CD 
could be produced, if, at each instant the coil AB became parallel to CD, 
the current were automatically reversed through it. With the single turn 
and a strong current, sufficient repulsive force would be produced to move 
it through 180°; if the current be now reversed it will receive a similar 
impulse and will be repelled through another 180°, and so on. There will 
thus be two reversals and two impulses given to the movable coil each 
revolution, and continuous rotation produced. The force producing the 
rotation wiU still be dependent upon the current in both coils as in the 
dynamometer. A uniform force for producing rotation would require 
several coils similar to AB arranged about a vertical axis, with their 
planes at angles to each other, so that as one coil moved away from the sta- 
tionary coil another would take its place. Such an arrangement would 
be practically a motor, the moving coils forming the armature and the 
stationary coil the field. A worm on the armature shaft engaging with 
the train of wheels of a cyclometer dial would record the number of revolu- 
tions, and since this number in an hour depends on the currents through the 
coils during that time the cyclometer dial could be calibrated in watt- 
hours, provided the speed were proportional to the power consumed. 

The Thomson watt-hour meter, of which an interior view is 
shown in Fig. 215 is a simple type of motor, driven by the 
electrical energy which it is to measure; its speed of rotation 



272 



LESSONS IN PRACTICAL ELECTRICITY 



during any period is proportional to the power in watts de- 
livered to the circuit during that time. The movable coil or 
armature revolves between two stationary coils with its axis 
at right angles to the axes of these coils. The movable coil is 
a spherical armature (Fig. 216) without an iron core, and the 
current through its coils is reversed automatically by the 
commutator, thus causing it to revolve. Current is led to the 

commutator by silver- 
tipped contacts or brushes. 
A worm on the upper end 
of the armature shaft en- 
gages a set of wheels which 
records the watt-hours on 
a dial. The armature is 
very light and delicately 
poised between jewel cen- 
ters, so that the friction 
is reduced to a minimum. 
The field of the watt- 
hour meter is produced by 
current in the stationary 
coils AA, placed one on 
either side of the armature 
B and connected in series 
with the line to which the 
meter is connected (Fig. 
217). The field strength 
is strictly proportional to 
the current in the main 
The armature (in series 




Fig. 215. — Thomson Watt-hour Meter. 



hne, since there is no iron in the field 
with a comparatively high resistance) is connected by means 
of the commutator and brushes across the line, just like the 
voltage coil in the indicating wattmeter, so that the current in 
the armature is proportional to the voltage across the line. 
Consequently the torque (turning effort) of the armature must 
be proportional to the product of the voltage and the current, 
or to the watts expended in the load. 

In series with the armature and resistance R (Fig. 217) is 
also connected an adjustable shunt field coil C, so placed as 



WATTMETERS AND WATT-HOUR METERS 273 



to strengthen the field set up by the main field coils. The func- 
tion of this coil is to compensate for the sHght friction in the 
rotating armature, and when properly adjusted, its position is 

such that the field . - - 

created by it will not ^ . i 

cause rotation of the 
armature when there 
is no current in the 
main field coils, but 
with the smallest cur- 
rent in the main 
coils, its field will just 
overcome the friction 
in the armature and 
cause it to rotate. 
If the meter runs 
when no current is 
being used, causing 
the meter to register 
more energy than 
the consumer actu- 
ally used, the meter 
is said to '^ creep." 
This will occur if the 




Fig. 216. — Armature, Commutator and 
Brushes of Watt-hour Meter. 



compensating coil C is too close to the 
main field coils. The coil is ad- 
justable in a plane parallel to 
that of the main field coils, so 
that it can be moved to and fro 
as the need may be. 

Since no iron is used in the 
magnetic circuit, the field is weak 
and the armature will develop 
little or no counter electromotive 
force (^313). The armature 
current, therefore, is independent 
of the speed of rotation,' and is 
constant for any definite potential applied at its terminals. 
Under these conditions the armature would revolve at an ex- 
ceptionally high speed, if there were no retarding force appHed 





— V 


v\rv 

R 

6000' 

A 


if 

I 


0000 

A 

n 


WoC 


\ 


i ^i 


Load 

— 1 — TT 


Lfn 


e 


1 1 ??? 



Fig. 217. — Circuits of Thomson 
Watt-hour Meter. 



274 LESSONS IN PRACTICAL ELECTRICITY 

to the armature; therefore, in order to reduce the speed and 
secure correct registration by the meter it is necessary to pro- 
vide some means for making the speed proportional to the 
torque. This is accomphshed by applying a load or drag, the 
strength of which varies directly as the speed. Such a control- 
ling force is obtained by causing an aluminum or copper disk 
attached to the armature shaft to rotate between the poles of 
stationary permanent horseshoe magnets, and cutting their 
magnetic lines of force as it revolves. Eddy currents (Tf 254) 
are induced in the disk, and the reaction of their magnetic field 
tends to retard the rotation. The amount of this retarding force, 
or drag, is directly proportional to the speed of rotation. Since 
the torque causing the armature to rotate is directly propor- 
tional to the magnetic fields of the currents in the two coils, and 
the retarding torque is also proportional to the magnetic field 
set up, the armature must rotate at such a speed that the elec- 
tromagnetic driving torque is exactly equal to the electromag- 
netic retarding torque. Then in a given length of time, the 
number of revolutions of the armature, and, therefore, the 
travel of the dial hands, will be proportional to the energy sup- 
plied. 

Watt-hour meters are made in different sizes according to 
the current-carrying capacity of the current coil. The amount 
of extra resistance in the armature circuit depends on the volt- 
age to which it is to be subjected. These meters are exten- 
sively used on commercial motor circuits and in individual 
house electric-light service, and are sensitive enough to record 
the energy through even a small-sized lamp when connected 
to the supply circuit. 

225. Sangamo Direct-Current Watt-Hour Meter. — The 
Sangamo direct-current watt-hour meter is a mercury type of 
meter, somewhat similar in principle to the direct-current 
commutator type, but instead of having a moving coil and 
commutator, its armature consists of a copper disk which 
revolves in a mercury chamber, the mercury forming part 
of the circuit. This arrangement practically eliminates com- 
mutator friction, and the armature is floated in the mercury 
chamber. The principle of operation may be understood by 
referring to Fig. 218, which shows the relations of the various 



WATTMETERS AND WATT-HOUR METERS 275 




Line 



Load 



w. 



parts, and also the voltage and current circuits of the meter. 
An electromagnet with poles N-S is energized by the poten- 
tial coil or shunt winding SC, connected across the line wires. 
The mercury chamber M is made of insulating material and has 
molded in it the contact ears Ei and E2 diametrically opposite 
each other, and also has molded in it above the armature 
space a spirally-laminated soft steel ring D, which acts as a 
return for the magnetic Hnes of force from the electromagnet 
N-S. The copper disk A is secured to the shaft S, which carries 
the worm W to drive 

the recording mechan- (TTW— _ -5L^ 

ism; at the upper end 
of the shaft is secured 
the aluminum disk B, 
revolving between the 
poles of the permanent 
magnets F F, for regu- 
lating the armature 
speed. The shaft is 
supported at the upper 
end by a jewel bearing. 
One end of each of the 
series coils CT connects to the mercury by the ears Ei, E2; the 
other ends of the winding connecting one to the line and the other 
to the load. The function of this series winding is to strengthen 
the field of the electromagnet as the load increases, and com- 
pensates for a falUng off in speed due to increased mercury 
friction. From Fig. 218 it will be seen that the magnetic flux 
produced by the potential coil. SC cuts or passes through the 
copper disk A, in order to complete its path through the soft 
steel ring D from the N-pole to the S-pole below. The disk, 
being in series with the load, is carrying a current wliich, 
due to the position of the contact ears, passes across the mag- 
netic field from the magnet poles N-S, at right angles to this 
field. Since a conductor free to move and carrying a current 
whose direction of flow is at right angles to a fixed field will 
tend to move out of that field, the disk A moves from its ini- 
tial position, and then the current entering at a new point on 
the periphery of the disk, causes it to be again impelled for- 



Fig. 218. — Arrangement of the Parts and 
Circuits of a Sangamo D. C. Watt-hour 
Meter. 



276 LESSONS IN PRACTICAL ELECTRICITY 

ward; this constant change in point of current entrance to 
the disk producing a continuous rotation. The torque is pro- 
portional to the current in the disk and to the magnetic field, 
the latter being proportional to the voltage of the circuit; 
therefore the torque is proportional to the power in watts. 
The speed is rendered proportional to the torque by means of 
the aluminum disk B as explained in K 224. 

Compensation of friction on Hght loads is provided for in 
this meter, but not shown in Fig. 218, by an adjustable shunt 
circuit connected across the armature at Ei and E2. This 




Fig. 219. — Registration Dials of a Watt-hour Meter. 

shunt circuit consists of a thermo-couple in series with an 
adjustable resistance; the thermo-couple is operated by a 
heating coil connected in series with the winding SO. The 
E. M. F. produced by the thermo-couple sends a current 
through the disk, thereby producing sufficient torque to over- 
come friction under light loads. 

226. Reading the Watt-Hour Meter. — The dials of an 
electricity or watt-hour meter are graduated in watt-hours or 
kilowatt-hours and read Hke the dials on a gas meter. The 
unit in which the measurement is made is usually marked on 
the dial face and would be watt-hours or kilowatt-hours. The 
dial face may contain four circles, as in Fig. 219, or five circles; 
however, the principle of reading either of them is exactly the 
same. In Fig. 219 the dial face contains four circles, the figures 
marked above each circle, such as 1000, etc., are the amounts 
recorded by a complete revolution of the pointer, therefore, one 
division on a circle indicates one-tenth of the amount marked 
about the circle. A complete revolution of the pointer on any 



WATTMETERS AND WATT-HOUR METERS 277 

circle moves the pointer on the next circle to the left,- one 
division; to illustrate: a complete revolution of the pointer 
on the '^10" circle moves the pointer on the '^100" circle one 
division and registers 10 kilowatt-hours. The pointers on the 
first and third circles turn clockwise, while the pointers on the 
second and fourth circles turn counterclockwise. 

In deciding the reading of a pointer, the pointer before it 
(to the right) must be noted, for unless the pointer before it 
has reached or passed ''o," or in other words, completed a 
revolution, the other has not completed the division on which 
it may appear to rest. For this reason ease and rapidity are 
gained by reading a meter register from right to left. To 
correctly read the sum indicated on the dial face of a watt-hour 
meter, begin with the circle on the right-hand side of the dial 
face, that is, the circle of lowest capacity, then note the readings 
of the second and third circles, and so on, putting the num- 
bers down in their, proper order, or from right to left. 

In Fig. 219 the statement of the register is 9659 kilowatt- 
hours. Wattmeter readings are cumulative, and to learn the 
amount of electrical energy consumed during any interval of 
time, it is necessary to subtract the reading at the beginning 
of the period from that taken at its close. Meters of large 
capacity are subject to a multiplying constant, such as 10, or 
some miiltiple thereof, and this value appears on the dial face; 
the registration of such meters must be multiplied by the con- 
stant to determine the actual consumption of electrical energy. 

The constant is the measure of the mechanical adjustment 
in the register of the meter and is the ratio of the true energy 
consumption and the registration of the dial hands. The con- 
stant is used to avoid a high speed of rotation, the adjustment 
is made by the manufacturer of the meter. 



QUESTIONS 

1. Describe an indicating wattmeter. 

2. Sketch in detail a Weston indicating wattmeter connected to a 
motor circuit so as to indicate the power being absorbed. 

3. What is the difference between an indicating wattmeter and a watt- 
hour meter? 

4. What is the principle of operation of a Thomson watt-hour meter? 



278 



LESSONS IN PRACTICAL ELECTRICITY 



5. .How is the proper speed of rotation and correct registration ob- 
tained in the watt-hour meter? 

6. A Thomson watt-horn- meter is found to register a small amount of 
energy after the load has been disconnected. What is the trouble and how 
could it be remedied? 

7. How does the Sangamo watt-hour meter differ from the Thomson 
watt-hour meter, and upon what principle does it operate? 

8. Indicate the positions of the pointers on the dials below for a read- 
ing of 253,400 watt-hours. 



1000.O0O 



100^00 



10.000 




iaooo.ooo 



1000 



LESSON XIX 



MEASUREMENT OF RESISTANCE 



Resistance Standards — Voltmeter and Ammeter Method of Measuring 
Resistance — Substitution Method of Measuring Resistance — Com- 
parative Drop Method of 'Measuring Resistance — Voltmeter Method 
of Measuring Resistance — Wheatstone Bridge Method of Measur-. 
ing Resistance — The Slide-Wire Bridge — Commercial Wheatstone 
Bridges and Portable Testing Sets — Ohmmeters — Questions and 
Problems. 

227. Resistance Standards. — The value of an unknown 
resistance may be measured by a direct application of Ohm's 
Law, or by comparison with a ''Standard" resistance, using 
the methods given below. 

The Standard ohm defined in If 63, as the resistance offered 
by a uniform column of mercury 106.3 centimeters long and 
weighing 14.4521 grams, is not a convenient standard with 
which to compare resistances in practice, therefore secondary 
standards, made of wire and standarized with great precision, 
are used commercially. The wire used must have a fairly high 
resistivity and a low temperature coefficient; 
therefore, these standards of resistance are made 
of manganin wire, which possesses these qualities. 
A number of resistance standards of various 
values when assembled in a single case are col- 
lectively called a resistance box, or sometimes a 
rheostat (If 75). 

Very low resistance standards of large current- 
carrying capacity have their coils immersed in 
oil and provided with four terminals, as in Fig. 
220. In this diagram A and B are the current 
terminals and are connected in series with the 
circuit, C and D are the potential terminals to which is con- 
nected the voltmeter or whatever potential device may be used. 

279 




Fig. 220. — 
Standard Re- 
sistance. 



280 



LESSONS IN PRACTICAL ELECTRICITY 



^® 




Fig. 22 L 



Voltmeter and Ammeter 
Method. 



228. Voltmeter and Ammeter Method of Measuring Resis- 
tance. — This is a very simple method for measuring an 
unknown resistance directly by Ohm's Law, requiring an am- 
meter, a voltmeter and a source of electricity. The unknown 
resistance, X, is connected in series with an ammeter and 

source of electricity as in 
Fig. 221, and a voltmeter is 
then connected across the 
terminals of that resistance. 
Simultaneous readings of 
both instruments are made; 
the value of the unknown 
resistance is then found by 
Ohm's Law. 

This method of resistance 
measurement is well adapted to practical work in the repair 
shop, the laboratory, or the central station for measuring the 
resistance of the field and armature windings of generators and 
motors, the resistance of 
incandescent lamps while 
burning, or the resistance of 
almost any electrical device. 
Fig. 222 illustrates the 
method of measuring the 
resistance of an incandes- 
cent lamp while burning, 
the ammeter is in series 
with the lamp, the voltmeter is connected across the lamp, and 
the resistance is then found by applying Ohm's Law. 

In using this method to measure the resistance of a wire or 
coils of wire, care must be taken not to pass a greater current 
through the wire than it will carry without undue heating, 
otherwise a higher resistance than the true one will be meas- 
ured. A milli voltmeter will give greater accuracy when the 
resistance is quite low, as, for example, the series field of a 
large dynamo which may have a resistance of perhaps 0.001 
ohm. On the other hand, when the method is applied to high 
resistances the current will usually be small and a milliam- 
meter can be used to advantage. 



V"/ 




\ V.M 


X 


Lamp(^ 


r 


f J Oenercffor 


b 


y 





Fig. 222. 



Measuring the Resistance 
of a Lamp. 



MEASUREMENT OF RESISTANCE -281 

Problem 102. — What is the resistance of the object X (Fig. 221) if 
the respective readings of ammeter and voltmeter are 4 and 36? 

E S6 

By Ohm's Law R = - = — = 9 ohms. 
■^ I 4 

Problem 103. — The resistance of a bonded rail is to be measm-ed by 
the voltmeter-ammeter method. The cm-rent through the rail and its 
copper joint is 500 amperes, the drop across the joint is 25 millivolts. What 
is the resistance in microhms? 

By Ohm's Law R = y = ^^ = 0.00005 ohm. 

By Formula (1) 0.00005 x 1,000,000 = 50 microhms. 

229. Substitution Method of Measuring Resistance. (Gal- 
vanometer and adjustable rheostat required.) — The unknown re- 
sistance X and the galvanometer G are connected in series with 
a source of continuous current (Fig. 
223) and the galvanometer deflection 



Uaaaaaaaa!^ viy 



R 



is noted. Then substitute for the 
unknown resistance X, a known 
adjustable resistance R (such as a 

resistance box) by moving switch S, I |||| 

and adjust the value of R until the 

galvanometer deflection is the same ^'^- ^^^'j^thod'^'^''^''''' 

as before. The resistance in the 

rheostat is now equal to the unknown resistance, since the 

current through the galvanometer is the same as before, and 

the pressure is also the same. 

Problem 104. — With the connections shown in Fig. 223 the deflec- 
tion of the galvanometer with the unknown resistance- in circuit was 25 
divisions. With the rheostat substituted it was found necessary to unplug 
47 ohms to obtain a deflection of 25 di\dsions. What is the resistance of 
the device? Ans. 47 ohms. 

230. Comparative Drop Method of Measuring Resistance. 

(A standard resistance or graduated rheostat and a voltmeter re- 
quired.) — This method is very convenient for many practical 
measurements. No ammeter is required. The standard and 
unknown resistances are connected in series and to a source of 
continuous current (Fig. 224). The drop in volts across each 
resistance, as measured by the voltmeter, is directly propor- 
tional to its resistance, since the current is the same through 



282 LESSONS IN PRACTICAL ELECTRICITY 

both resistances. The drop on the standard resistance also bears 
the same relation to the drop on the unknown resistance as the 
value of the standard resistance bears to the value of the un- 
known resistance, or, calling the unknown resistance X, then: 

drop on standard _ resistance of standard 
drop on X resistance of X ' 

or 

resistance of standard x drop on X . . 

drop on standard 

A high-resistance galvanometer, the deflections of which are 
proportional to the current, may be used instead of the volt- 
meter and the value of the 
v.m7 deflection substituted in the 

formula. The most accurate 




JWWWW^ 



Standard Unknown 

Resistance Resistance 



results are obtained when 
the standard resistance is 
selected in value as near as 
possible to the supposed 
Fig. 224. — Comparative Drop Method, value of the unknown resis- 
tance. If the current is not 
very steady several readings should be taken for each measure- 
ment and the average value used in the formula. With suit- 
ably selected standards this method is adapted for measuring 
either high or low resistances with accuracy. 

Problem 105. — With the connections shown in Fig. 224 the drop on the 
standard resistance of 5 ohms was 2 volts, while the drop on the unknown 
resistance was 10 volts; what is the value of the unknown resistance? 

By Formula (84) X = ^-^^ = 25 ohms. 

Li 

231. Voltmeter Method of Measuring Resistance, (yolt- 
meter of known resistance required.) — This method is especially 
adapted for measuring high resistances, such as insulation 
resistance of wires, etc. The voltmeter is connected in series 
with the unknown resistance X across the source of E. M. F., 
which should be as high as possible, wdthin the limits of the 
voltmeter scale. A switch or key K is connected across the 
resistance X so that it may be short-circuited, Fig. 225. A 



MEASUREMENT OF RESISTANCE ' 283. 

reading of the voltmeter is taken when the key is closed, and 
the value of the indication is represented by the letter V. 
With switch K open, the unknown resistance X is inserted in 
series with the voltmeter, and the voltmeter indication is again 
noted, calling it Vi. 

With the switch K closed, the voltmeter reading V repre- 
sents the voltage across itself, that is, across its resistance r. 
When the switch is open the voltage at the 
generator terminals is distributed across ^.y^\^ 
resistance X and the voltmeter in direct |V>^ 
proportion to their separate resistances, 
since they are both in series across the 
generator terminals (H 230). In this con- 
dition the reading Vi when the switch K is ^ig. 225. — Meas- 
open also represents the voltage across the urement of Resistance 
voltmeter, but the difference between V by the Use of a Volt- 
and Vi represents the voltage across the 
resistance X. Since with the switch open a simple series circuit 
is formed in which the resistance of each part is proportional to 
the voltage across that part, the resistance of X may be cal- 
culated from the following proportion: 

X V - Vi 
X:r=V-Vi:Vi, or ± = ^L^. 

r Vi 

therefore, 

X = r('^-l'\ (85). 



&-0 



Problem 106. — When the voltmeter in Fig. 225 is directly connected 
across the source of E. M. F. it indicates 110 volts; when placed in series 
with the unknown resistance it indicates 4 volts. What is the value of the 
unknown resistance if the voltmeter has a resistance of 150,000 ohms? 

By Formula (85) X = r (^ " V = 150,000 (-^— - l) = 150,000 X 

(27.5 - 1) = 150,000 X 26.5 = 3,975,000 ohms, or 3.975 megohms. 

A modification of this method suitable for the measurement 
of very high resistances is the so-called direct deflection method 
which employs instead of the voltmeter of Fig. 225 a sensitive 
galvanometer whose constant is known (Lesson XVI). No 
short-circuiting key K is used, otherwise the circuit is the same 



284 . 



LESSONS IN PRACTICAL ELECTRICITY 



as Fig. 225. Thus, if the galvanometer gives a deflection of 12 
divisions for one volt through 1 megohm, then if 500 volts are 
used in measuring the insulation of cable and the galvanometer 
gives 150 divisions deflection, it is evident that the insulation 
resistance of the cable is 

500 12 .^ , 

X = 40 megohms. 

1 150 ^ 

232. Wheatstone Bridge Method of Measuring Resistance. ■ — 

To measure resistance with extreme accuracy, the Wheatstone 
bridge is universally used. The Wheatstone bridge is con- 
structed in several different forms which will be described in 
the following paragraphs. The simplest form and one in 
which the circuits are easily traced is the lozenge form illus- 




226. — Lozenge Form of 
Wheatstone Bridge. 



Fig. 227. — Circuit of Wheatstone 
Bridge. 



trated in Fig. 226. It consists of a diamond-shaped arrange- 
ment of metallic wires or strips provided with binding posts 
as shown, the wires being of sufficient area to insure negligible 
resistance. 

To make a resistance measurement with the lozenge bridge, 
connections are made as in Fig. 227 in which A, B, C and D 
are called the arms of the bridge. The gaps in the A and B 
arms are bridged by standard resistances, to the C arm is con- 
nected a rheostat, and the unknown resistance is connected to 
the D arm. A current from a battery is sent into the bridge 
at the post 1, at which point it divides into two parts: one part 



MEASUREMENT OF RESISTANCE 285 

flowing in the branch circuit consisting of resistances A and C, 
the other part flowing through the branch consisting of resis- 
tances B and D, the current from both branches uniting at 
point 2 to return to the battery. A galvanometer G is con- 
nected between the two branch circuits at points 3 and 4, and 
keys K and K' are connected respectively in the battery and 
galvanometer circuits. 

The theory of the bridge is as follows: when a current flows 
through a circuit there is a drop in potential across each part 
of the circuit proportional to the resistance of that part and 
to the current in it. With the galvanometer key K' open, the 
current will be the same through all parts of the upper branch 
circuit of Fig. 227, say Ii; then the drop of potential from 1 to 
3 is the product of resistance A ohms and of Ii amperes, or 
A X Ii volts, in accordance with Ohm's Law, and likewise, the 
drop from 3 to 2 is C x Ii volts. Again, if the current in the 
lower branch circuit be I2, then the drops across coils B and D 
will be respectively B x I2 and D x I2 volts. These four 
drops of potential will usually have different values; for ex- 
ample, the potential between 1 and 3 will be different from that 
between 1 and 4, in consequence there will be a difference of 
potential from 3 to 4. On depressing the galvanometer key 
K', a current will flow through the galvanometer as a result 
of that potential difference, and the moving element of the 
instrument will be deflected. If, however, the resistances are 
so proportioned with respect to each other that the drop from 
1 to 3 (namely A x Ii) will equal the drop from 1 to 4 (namely 
B X I2) then on closing the key K' no current will flow through 
the galvanometer because there is no difference of potential 
between its terminals, 3 and 4. When this condition obtains, 
it is evident that 

A X Ii = B X I2, 
and also C x Ii = D x I2. 

Dividing member by member, there results • 

A X Ii _ B X I2 

from which _ = _, 

C D' 



286 



LESSONS IN PRACTICAL ELECTRICITY 



which expresses the relationship between the four resistances 
in order that the galvanometer will show no deflection. In 
practice the resistance in the A and B arms, called the bridge 
arms, are adjusted to a certain ratio dependent upon the 
approximated value of the unknown resistance, and the varia- 



Dan/e// Cell 



Rheosfaf. 




-Double 
Contact Key 



Coil ofUnknoivn 
Resistance 
■Defector Galvanometer 



Fig. 228. — Student's Wheatstone Bridge (Lozenge 
Pattern) with the Apparatus Required for Measuring 
Resistance. 



ble resistance in the C arm is adjusted until, on closing key K', 
the galvanometer gives no deflection, and the bridge is said to 
be balanced. If the value of A, B and C are known, the value 
of D can be determined by the following formula deduced from 
the foregoing proportion: 



B xC 



D = 



(86). 



MEASUREMENT OF RESISTANCE 287 

The connections and apparatus required for making a re- 
sistance measurement with the lozenge form of bridge are 
illustrated in Fig. 228. The apparatus illustrated comprises 
the following parts: Daniell cell, adjustable graduated rheo- 
stat, two standard resistance spools (those shown have ten 
ohms each), detector galvanometer, the resistance to be meas- 
ured (in this case a solenoid), and a double-contact key which 
combines the two separate keys shown in Fig. 227. This 
double-contact key practically consists of two button switches 
mounted one over the other on the same base; the upper 
switch is connected to the two adjacent posts marked B, and 
closes the battery circuit when a shght pressure is apphed. 
The lower switch is connected to the other two posts marked 
G, and is inserted in series with the galvanometer (Fig. 228). 
When the knob is depressed two independent circuits are 
closed, first the battery and then the galvanometer circuit. 
On releasing the knob the galvanometer circuit breaks first. 
The battery circuit must always be closed before the galva- 
nometer circuit in order to allow the current to become steady 
before closing the galvanometer key, hence the use of the 
double-contact key. 

Six resistance standards, made up in convenient form and 
provided with wire terminals to shp into the posts of the A 
and B arms, are furnished with this particular bridge. There 
are two 1-ohm, two 10-ohm, and two 100-ohm spools; the 
proper selection of these standards is given later. 

The balancing of potentials in a Wheatstone bridge may be 
practically illustrated by the use of a voltmeter and a number 
of incandescent lamps connected in the manner shown in 
Fig. 229, Experiment 79. 

Experiment 79. — In Fig. 229 there are shown nine 50-volt carbon- 
jBlament lamps connected so as to form the four arms of the Wheatstone 
bridge, and 125 volts from a generator are applied to the points 1 and 2. 
Each lamp will be assumed to have a constant resistance of 50 ohms 
irrespective of the amount of current flowing through it. 

In the upper branch of the divided circuit, there are two lamps in series 
in the A arm, making a total resistance of 100 ohms, and in the C arm 
there are two lamps in parallel, making a joint resistance of 25 ohms; 
therefore, the total resistance of A and C in series is 125 ohms. With 125 
volts maintained across points 1 and 2, the branch AC will receive one 



288 



LESSONS IN PRACTICAL ELECTRICITY 



\^mpe^_^ 



ampere, and the potential across A will be 100 volts and across C 25 volts. 
The lamps in the A arm will burn at normal candle power, but the lamps in 
the C arm will burn dimly since they get only 0.5 ampere each. In the lower 
branch the B arm has 4 lamps in series making its resistance 200 ohms, and 
D has one lamp of 50 ohms; therefore, the total resistance of B and D 
in series is 250 ohms and the current through this branch will be 0.5 am- 
pere, all lamps burning dimly. The potential across B will equal 100 volts, 
the same as the potential across A, and that across D will be 25 volts, or 
the same as the potential across C. If a voltmeter is now connected to 

points 3 and 4, as shown, it will not give 
any appreciable deflection, since the po- 
tential across 1-3 is the same as that 
across 1-4, namely 100 volts; and the po- 
tential across 3-2 is the same as that across 
4-2, or 25 volts. 

This balancing of potentials is due to 
the fact that the value of resistance A 
bears the same ratio to that of B, as the 
value of resistance C bears to that of D. 
The student should measure with the volt- 
meter the voltage across each arm of the 
bridge, and across points 3-4 to verify the 
above statement; then take similar meas- 
urements, after having unbalanced the 
potentials by taking one of the lamps in 
the C arm out of that circuit. When the 
voltmeter is connected to points 3 and 4 
under the latter condition it will show a 
difference of potential to exist between 
these two points. 

The foregoing experiment may be modi- 
fied by using one 110-volt lamp in each arm of the bridge (all lamps of the 
same type) and using 110 volts across points 1 and 2. If all the lamps have 
the same resistance the bridge will be balanced and a voltmeter will not 
indicate when connected across points 3 and 4; the bridge may be un- 
balanced by replacing the lamp in one arm by one of a different type or 
of different voltage. 

Operating the Bridge. — Make the bridge connections as 
given above and shown in Fig. 228. Suppose the unknown re- 
sistance, a coil of wire connected at D, to be about 20 ohms. 
Connect a 10- ohm spool in arms A and B. See that all con- 
nections are bright and tight. Insert resistance in the gradu- 
ated rheostat to the value of what you approximate D will 
measure. Depress the double-contact key and note the direc- 
tion of deflection of the galvanometer needle, say to the left. 




/^Amperes ^^--^ QenerartQr 



Fig. 229. — Lamp Analogy of 
the Wheatstone Bridge. 



MEASUREMENT OF RESISTANCE 289 

Release the key and add more resistance to circuit C. If, on 
depressing the key, the deflection is still to the left hut less than 
before, release the key and add more resistance. If, on the next 
trial, the needle swings to the right, too much resistance has 
been added and some must be taken out of the rheostat circuit. 
Proceed in this manner till a balance is obtained. In the above 
case the needle swinging to the right of zero means that the 
rheostat's resistance must be decreased while the needle swinging 
to the left of zero indicates too low a resistance in the rheostat. 
With the same pole of the battery always connected to the 
same bridge post, and likewise with the galvanometer, this 
relation of the needle's deflection will always hold good, and 
in such a case could be marked on the instrument, as is done 
in the portable bridge sets. 

Suppose a balance is obtained when 18 ohms are in the 
rheostat circuit, then by Formula (86) 

^ B xC 10x18 ,„ , 

D = — : — = = 18 ohms. 

A 10 

When the A and B arms have equal resistances they will 
always cancel in Formula (86), so that the unknown resis- 
tance is then equal to the amount inserted in the rheostat cir- 
cuit, and can be read directly from it without reference to 
the formula. With equal resistances in the A and B arms, 
which should always be as near as possible to the unknown 
resistance, the maximum resistance that the bridge will meas- 
ure is limited to the resistance contained in the rheostat. 

To Measure a High Resistance. — • The value of the resis- 
tance in the A arm should be low, since from Formula (86) it 
will be observed that the value of the resistance in the A arm 
is the divisor; consequently if a low-resistance spool is selected 
for it and a high-resistance spool for the arm B, the quotient 
will be high. For example, let B = 100 ohms and A = 1 ohm, 
and suppose that balance against some unknown resistance was 
obtained when 150 ohms had been inserted in the rheostat, then 

^ BxC 100x150 ,_„„„ , 
D = — - — = = 15,000 ohms, 

j\. i 

or the bridge is capable of measuring a much higher resistance 
than the rheostat may contain. 



290 LESSONS IN PRACTICAL ELECTRICITY 

To Measure a Low Resistance. — The A arm should have a 
large resistance and B small, hence select spools for arms A 
and B accordingly. For example, let arm B = 10 ohms and 
A = 100 ohms, and assume that balance obtains against some 
unknown resistance when 2 ohms are inserted in the rheostat, 

^^^^ ^ BxC 10 x2 20 .^, 

D = — - — =. = = 0.2 ohm, 

A 100 100 

or the bridge will measure a much lower resistance than the 
rheostat may contain. Suppose a balance is obtained in another 
measurement when B = 1, A = 100 and C = 3; then 

^ BxC 1x3 ^^. , 

^=^-=Too- = '-^'"^"^- 

The selection of spools for the greatest accuracy in measure- 
ment depends upon the resistance of the galvanometer and 
the internal resistance and E. M. F. of the cells used with the 
bridge, so that no specific rule can be given beyond the vary- 
ing of the ratios, as here given. 

233. The Slide- Wire Bridge. — A simple form of sHde-wire 
bridge for measuring resistance is depicted in Fig. 230. A 
piece of high-resistance wire of uniform cross-section is stretched 
between binding posts 1 and 2, and takes the place of resis- 
tances A and C in Fig. 227. Directly under the wire is a double 
scale graduated in 1000 equal divisions with zero at either 
end, to facilitate taking readings from either point, 1 or 2. 
The letters and figures indicate the same points on this form 
of bridge as on the lozenge form of Fig. 227. Both forms of 
bridge operate upon the same principle, but in the slide-wire 
form the potentials are balanced by moving the slider S along 
the wire between posts 1 and 2, thus decreasing or increasing 
the resistances of A or C as desired. A standard resistance 
spool is inserted in the binding posts at B (Fig. 230) and the 
unknown resistance is connected to the posts at D. The 
battery is connected across points 1 and 2, as before, and one 
galvanometer terminal is joined to post 4 while the other is 
connected to the flexible-wire slider S. This slider is moved 
along the wire 1-2 till some point, as 3, is found where the 
galvanometer needle is not deflected; then the length 1-3, or 



MEASUREMENT OF RESISTANCE 



291 



A, and length 3-2, or C, are read from the scale. The value 
of the unknown resistance D is calculated from the proportion : 

resistance B resistance D ,g„x 



length A 



or 



D 



length C 
BxC 



The lengths of A and C are used instead of actual resistances 
as with the lozenge form of bridge, since the resistance is pro- 



Standard 
Resistance 



Unknown 
Resistance 




Qalvanomefer 



Fig. 230. — Student's Slide-wire Bridge. 

Complete connections for measuring an unknown resistance are depicted. 

portional to the length. It will be observed that the last 
equation is identical with Formula (86). 

Several different spools are furnished with the bridge, such 
as 1, 10, 100 and 1000 ohms, and the proper spool to be inserted 
at gap B should be as near in value to the resistance to be 
measured as can be approximated before measurement. The 
error in measurement is less when this is the case. 

In moving the slider over the bridge wire care should be 
exercised not to scrape the wire, since the accuracy of meas- 
urement depends upon the uniformity of cross-section of the 
bridge wire. It is best to make several trial contacts at differ- 
ent points and note the direction of the needle's deflection, 
instead of running the shder along the wire. About the same 
pressure of the hand should be appUed in making contact with 
the shder in different measurements. The shde wire form of 
Wheatstone bridge is adapted for measuring low resistances; 



292 



LESSONS IN PRACTICAL ELECTRICITY 



it is not as accurate, however, as the other forms, due to the 
wearing of the sHde wire and its comparatively low resistance. 

Problem 107. — The resistance of a spool of wire approximated as 
20 ohms is connected to a slide-wire bridge for measm-ement, a 10-ohm 
spool is selected for the B arm of the bridge and the following data is re- 
corded when balance is obtained: A = 350 scale divisions read from the 
left-hand zero mark, C = 650 divisions read from right-hand zero mark. 
What is the value of the unknown resistance? 



By Formula (87) D 



B xC 10 X 650 
A ~ 350 



18.57 oh] 



Problem 108. — What is the value of an unknown resistance measured 
by the slide-wire bridge when B = 1 ohm, A = 900 divisions, and C = 100 
divisions. 



By Formula (87) D = 



B X C 1 X 100 



900 



= 0.11 ohm. 



234. Commercial Wheatstone Bridges and Portable Testing 
Sets. — In practice the commercial form of Wheatstone bridge 
is seldom made in the lozenge shape illustrated in Figs. 226 and 
227, for that is merely a laboratory form used in teaching the 
principles involved. The commercial forms of Wheatstone 

bridge or ''portable testing 
sets" as they are some- 
times called, consist of the 
bridge and rheostat arms 
mounted in a box usu- 
ally with a galvanometer, 
a battery and two keys. 
With these portable testing 
sets resistances varying 
from a fraction of an ohm 
to millions of ohms can be 
measured. 

Post-Office Bridge. — One of the older forms- of portable 
testing sets, the ''Post-Office" pattern of Wheatstone bridge, 
is shown m Fig. 231. It consists of an arrangement of coils 
and brass blocks forming three, arms of the Wheatstone bridge, 
resistance coils being inserted in the circuit by removing tapered 
plugs from the tapered holes formed between adjacent blocks, 
as in the plug type of rheostat shown in Fig. 67. This testing 




Fig. 231. — ''Post-OfRce" Pattern of 
Wheatstone Bridge. 



MEASUREMENT OF RESISTANCE 



293 



set requires a separate battery and galvanometer, whereas in 
most portable testing sets the battery and galvanometer are 
also contained within the case. 

The general plan of the ''Post-Office" form of bridge and its 
connections are shown in Fig. 232, in which the letters and 
figures correspond to similar ^ 

parts in the diagrams of the 
lozenge form of bridge (Figs. 
223 and 227) so that the lozenge 
may be traced out, though the 



e O0O88000 




232. — Connections of- 
Office" Bridge, 



parts are not arranged in the 
form of a lozenge. The current 
from the battery divides at 
point 1 and unites again at point 
2, and the galvanometer is con- 
nected across points 3 and 4 as 
in Fig. 227. Both the A and B arms are provided with four 

different resistances each, 
only one being used in each 
arm at any one time. The 
method of operating this 
bridge and the selection of 
resistance values of the A and 
B arms are as given in H 232. 
For measuring low and me- 
dium resistances one or two 
cells in series may suffice to 
operate the bridge. The 
higher the E. M. F. used the 
more accurate will be the re- 
sults. For very high resis- 
tances, such as insulation 
resistance, a large number 
of cells is employed. 
Queen- Acme Bridge. — An early commercial form of portable 
testing set, containing the battery and galvanometer within 
the case, is shown in Fig. 233, and is known as the Queen-Acme 
testing set. There are three rows of blocks, the center row 
constitutes the bridge arms and the outer rows, joined together 




Fig. 233. — Self-contained Bridge or 
Portable Testing Set. 



294 



LESSONS IN PRACTICAL ELECTRICITY 



by a copper bar connecting the right-hand blocks, constitute 
the rheostat, whose resistance can be varied from 1 ohm to 
11,110 ohms by removing the proper plugs. In the simplified 
diagram of the connections and circuits of the Queen-Acme 
testing set (Fig. 234) the blocks A, B, R and X form a commu- 
tator, the function of which is merely to transpose the two 
bridge arms A and B for various measurements by means of 
two tapered plugs. 

To make a resistance measurement with this set, the un- 
known resistance is connected to the large binding posts at 

the left-hand side of the in- 
A.vvi^ T^^x strument and the + terminal 

of the battery connected to 
the battery post marked +, 
set the commutator plugs ac- 
cording to arrow H (or arrow 
L) as indicated on top of the 
set. If the unknown resis- 
tance is thought to be higher 
than 6100 ohms, set the com- 
mutator plugs in the direc- 
tion indicated by arrow H; if 
the unknown resistance is lower" than 1100 ohms, follow the 
direction indicated by arrow L, Fig. 234; and if the unknown 
resistance is between 1100 and 6100 ohms the commutator plugs 
could be set to follow either arrows H or L. In selecting the 
resistance values of the A and B arms for this testing set, the 
value of A should be equal to or smaller than B. Having set 
the commutator plugs and inserted the proper resistance values 
in the A and B arms, remove plugs from the rheostat until the 
aggregate resistance unplugged is equivalent, as nearly as may 
be approximated, to the unknown resistance. Depress the 
battery key and, holding that down, momentarily press the 
galvanometer key. If the galvanometer needle swings toward 
the side of the scale marked with a + sign, the resistance un- 
plugged in the rheostat is too high and should be reduced. If 
the deflection is toward the - side, the resistance in the rheostat 
is too low and should be increased; the resistance in the rheo- 
stat being adjusted in this way until a balance is obtained. 




Fig. 234. 



Scheme of Queen-Acme 
Bridge. 



MEASUREMENT OF RESISTANCE 



295 



mwrnrnw 



If the commutator plugs have the position of arrow L, then 
the unknown resistance D = — x C, where C = value of re- 

sistance in the rheostat; if plugs have the position of arrow 
H, then D = ^ x C. 

Decade Portable Testing Sets. — In the decade form of testing 
set, the resistance coils that constitute the rheostat part of 
the set are arranged in equal series groups of nine or 10 
coils in series in each group ; 
that is,' there are nine or ten 
1-ohm coils for units place, 
nine or ten 10-ohm coils for 
the tens place, nine or ten 
100-ohm coils for the hun 



dreds place, and so on; each ^-fel H^[^H®H[3S]M 
group of coils of the same UUUUUUUUUU 

value is designated Si- decade. 

In this form of bridge, re- ^'S- 235- - go^H^^'^ «f 10-coil 
sistance is inserted in the 

circuit by placing a plug in the hole instead of removing the plug. 
The coils are connected in series through small brass blocks that 
face one long brass bar as illustrated in Fig. 235, and the resis- 
tance value in any one decade is obtained by inserting between 
the bar and a block, one, and only one, plug. With several 
decades in series any value up to the limit of the set can be 
read off directly from the position of the plugs, without any 
addition whatever. Thus, in Fig. 235 the resistance between 
the + and - terminals for the two decades is 35 ohms. This 
decade arrangement avoids the disadvantage of the previously- 
described bridges in that the latter requires a large number 
of plugs to short circuit the resistance coils not in use (which 
introduces an element of uncertainty as to the resistance of 
the plug contacts) and necessitates adding up the values of all 
the unplugged resistances in order to determine the total 
resistance in the circuit. 

An improved form of decade testing set, devised by the Leeds 



296 



LESSONS IN PRACTICAL ELECTRICITY 




& Northmp Co. and used in some of the sets manufactured 
by them, combines the advantages of the above form of decade 
arrangement with the need of but few coils. In these sets 
four coils are in series in each decade instead of 
nine : — in the units decade there are two 3-ohm 
coils in series with a 2-ohm and a 1-ohm coil, 
making a total of 9 ohms; in the tens decade 
there are one 10-ohm, one 20-ohm and two 30- 
ohm coils; and so on. The method of connect- 
ing these coils in a decade so as to obtain any 
value within the range of that decade is shown 
in Fig. 236, the circles in the diagram represent- 
ing two rows of ten brass blocks each. If a plug 
is inserted between- the first two blocks at the 
top of the rows the resistance value would be 0, 
if the plug is inserted between the blocks in 
the second horizontal line 1 ohm is obtained, if 
the blocks in the third horizontal line be con- 
nected 2 ohms, and so on; the total resistance 
of 9 ohms being obtained when the plug is in the 
ninth or last pair of blocks, which have no con- 
nections. The coils in each de- 
cade are connected in this man- 
ner and the decades connected 
in series so that the total range 
in, say, four decades, is 9999 
ohms, obtainable in one-ohm 
steps. 

A plug-type decade pattern of 
Wheatstone bridge, using four 
coils in a decade as described 
above, is shown in Fig. 237; in 
these sets a special arrangement 
of the resistance coils forming 
the ratio arms A and B of the 
bridge is such as to require only 
one plug in each arm, instead of three, as in the "Post-Office" 
bridge and the Queen- Acme testing sets. In the plug decade 
set (Fig. 237) each of the six ratio coils has one of its terminals 



Fig. 236. — 
Connection of 
4-coil Decades. 




Fig. 237. — Leeds and Northmp 
Decade Bridge. 



MEASUREMENT OF RESISTANCE 



297 




Fig. 238. —Leeds and North- 
rup Decade Testing Set. 



connected to a common center which leads to the galvanometer, 
while the other terminal of each coil is connected to an indi- 
vidual block, there being one block for each coil. The bar B on 
one side of these blocks is joined to 
the rheostat and the bar A on the 
other side to one of the posts marked 
^'X" where the unknown resistance 
is connected. To insert a resistance 
in the A arm, a plug is inserted be- 
tween bar A and one of the central 
row of blocks that will give the 
desired resistance value; a plug in- 
serted between bar B and one of the 
other blocks in the center row will 
insert a resistance coil in the B arm. 
With the set shown" in Fig. 237 a 
separate battery and galvanometer 
are used ; when these are connected 
to the posts marked Ba and Ga respectively and the unknown 

resistance is joined to posts X, the 
regular Wheatstone bridge cir- 
cuits are formed. This set may 
also be used as a rheostat alone 
when connections are made to 
the two posts at the upper right- 
hand corner of the set. 

A plug decade portable testing 
set containing a battery, galva- 
nometer and the necessary keys, 
in addition to the plug decade 
rheostat and ratio coils as de- 
scribed above, is shown in Fig. 238, 
A form of portable testing set 
that is rapidly replacing the plug 
decade set is the "Dial" decade set (Fig. 239) because the 
dial control of resistances is quicker and more convenient than 
the plug control. In this set there is a dial type Wheatstone 
bridge, consisting of ratio arms and a four-dial decade-type 
rheostat, a galvanometer, a battery and two keys. The two 




Fig. 239.— Dial Type Wheatstone 
Bridge or Testing Set. 



298 



LESSONS IN PRACTICAL ELECTRICITY 




Fig. 240. — Roller-Smith Ohmmeter (Com- 
bined Telephone and Galvanometer Type). 

Operates like a slide-wire bridge. 



ratio coils are controlled by one dial, which arrangement adds 
materially to the convenience of the operator for it determines 
at once the value by which the rheostat reading should be multi- 
plied. The multiplying values are stamped on the ratio dial, and 

are 0.001, 0.01, 0.1, 1, 
10, 100, 1000, giving the 
usual ratio range . With 
this form of bridge a 
balance may be ob- 
tained very quickly. 

235. Ohmmeters. — 
Instruments for the 
direct measurement of 
resistance, called ohm- 
meters, are of two 
general types. One 
type operates on the 
principle of the slide- 
wire bridge (that is, po- 
tentials are balanced), the balanced condition being indicated 
by a galvanometer or a telephone 
receiver. The scale under the 
slide wire is laid off in ohms (or 
in per cent of a fixed resistance 
value) so that the value of the re- 
sistance being measured is read 
directly in ohms. Fig. 240 shows 
a slide- wire ohmmeter of this type 
suitable for locating line breaks, 
grounds and crosses, for measur- 
ing resistance of electrolytes, etc. 
The principle of operation of this 
instrument is the same as that of 
the slide- wire bridge ( H 233) . 

The second type measures the 
resistance automatically by means 
of a movable coil which carries a pointer sweeping over a 
scale graduated in ohms, so that the value of the resistance 
connected to the instrument is read directly from the scale, 




Fig. 241. 



— Weston Ohm- 
meter. 



MEASUREMENT OF RESISTANCE 



299 



no calculations being required. The Weston direct-reading 
ohmmeter, of which an external view is shown in Fig. 241 and" 
its construction and circuits in Fig. 242, is an instrument be- 
longing to the second type above mentioned. In mechani- 
cal construction, the instrument is practically the same as the 
Weston D. C. voltmeter or ammeter, that is, it contains a 



Qji To Battery 



^^^.Jcrj^ for Adjusting 
^ \ [ ^ Magnetic Shunt 

To Battery-\^ 




Low Range- 



KD 



To Resistance 
to be measured 



To Resistance 
to be measured 



Fig. 242. — Construction and Circuits of the Weston Ohmmeter. 

horseshoe permanent magnet, provided with soft iron pole pieces 
between which is pivoted the movable coil carrying the pointer. 
The winding of the movable coil is divided into two parts by 
means of a tap at the center of the winding, and these two 
parts are included one in each of two branch circuits, the de- 
flection of the movable coil depending upon the currents flowing 
through the parts of its winding, which currents are propor- 
tional to the resistances connected to the branch circuits. By 



300 



LESSONS IN PRACTICAL ELECTRICITY 



tracing the flow of current from the upper right-hand battery- 
post of Fig. 242 it will be found that the current entering the 
coil at the top will divide and flow through the parts of the coil 
winding in opposite directions, a part of the total current flow- 
ing through resistance 1 and back to the battery, and the other 
portion of the current flowing through resistances 2 and 3 (if 

the plug is in the low- 
range block of the plug 
switch) and through 
the unknown resis- 
tance back to the bat- 
tery. Fig. 243 shows 
the same connections 
more clearly, all con- 
struction details being 
omitted. It will be 
seen, herefrom that 
the current through 
the upper portion of 




Fig. 243. — Electrical Scheme of the 
Weston Ohmmeter. 



the movable coil winding and resistance 1 will remain the same; 
whereas the current through the lower portion of the coil wind- 
ing, resistances 2 and 3, and the unknown resistance X in 
series, will depend upon the value of the unknown resistance. 

The current in the upper half of the divided circuit (Fig. 
243) will remain the same under a constant E. M. F., and the 
direction of this current in the coil is such as to move it in a 
direction to sweep the pointer across the scale. The current 
in the other portion of the movable coil is in the opposite direc- 
tion and consequently opposes the motion of the coil, its mo- 
tion is then the resultant of the two magnetic forces produced 
in the two parts of the coil. With an unknown resistance of 
a high value connected to the instrument the current in the 
lower half of the movable coil would be weak, and the mag- 
netic force of the other half of the coil would practically be 
unopposed, thus producing a large deflection. If the unknown 
resistance is low then the opposite effect is produced, since 
the current and resulting magnetic force in that half of the 
movable coil which is in series with the unknown resistance 
will be increased, thus setting up a greater opposing force. 



MEASUREMENT OF RESISTANCE 



301 




Fig. 244. — "Megger" Testing Set. 

For measuring high resistances. 



Resistances 1, 2 and 3 in Figs. 242 and 243 are so propor- 
tioned that the resultant ampere-turns on the coil are zero 
when the unknown resistance X is zero. R^esistance 4 has a 
value in ohms equal to the 
full-scale value of the in- 
strument and may be con- 
nected in the circuit by 
means of the plug switch, 
its function being to check 
the instrument at its top 
mark at any time. If, due 
to changes in the battery 
E. M. F., the top mark in- 
dication is not exactly 
correct, it may be made 
so by adjusting the self- 
contained magnetic shunt 
(Fig. 242) by turning the 
thumb screw at the top of 
the instrument. 

Weston ohmmeters are made with double ranges, the plug 
switch serving to make the change from one range to the other. 

The instruments 
may be operated 
with ordinary dry 
cells, four cells for the 
high-range and two 
cells for the low- 
range instruments. 
To measure a re- 
sistance with this in- 
strument, connect a 
battery to the proper 
binding posts and 
the unknown resist- 
ance to the two bind- 
ing posts provided 
for the purpose, press the contact key and read the value of 
the unknown resistance in ohms directly from the scale. 




Fig. 245. — Magnetic Circuit and Electrical 
Connections of " Megger" Testing Set. 



302 



LESSONS IN PRACTICAL ELECTRICITY 



An instrument that will measure higher resistances than 
the Weston ohmmeter is the instrument sold under the trade- 
name of '^ Megger," by James G. Biddle of Philadelphia, Pa. 
The '^ Megger" testing set consists of a direct-reading ohmmeter 
and a hand-driven direct-current generator assembled in a 

portable box (Fig. 244). An 
understanding of the opera- 
tion of the set can be ob- 
tained by considering Fig, 
245, which §hows the es- 
sentials of the magnetic cir- 
cuit and of the electrical 
connections. Herein MM 
are two permanent bar 
magnets, between the poles 
of which at one end is the 
armature D of the genera- 
tor, while at the other end 
is the moving indicating 
system of the ohmmeter. 
This system is made up of 
three coils. A, B and B' 
rigidly fixed together, and 
freely rotating about the 
axis O, without the direc- 
tive influence of any con- 
trolling springs. The de- 
tails of construction of the 
movable element are illus- 
trated in Fig. 246. 
If nothing is connected across the external terminals, and 
the generator is operated at proper speed by the small crank 
at the right-hand end of the set, as shown in Fig. 244, current 
from the generator will flow only through the two coils B and 
B' connected in series (Fig. 245). The electrical reaction thus 
set up drives these coils to a position where minimum flux 
from the permanent magnets passes through them; that is, 
directly opposite the gap in the C-shaped iron piece about 
which the coils A and B' move. The pointer then stands 




Fig. 246. 



Moving System of the 
''Megger." 



MEASUREMENT OF RESISTANCE 303 

over the line on the scale marked '^ Infinity," at the extreme 
upper end of the scale. Now, if a suitably high resistance 
is connected to the external terminals, the current from the 
generator has two paths open to it and will divide, part pass- 
ing through coils B and B' as before, and part through coil 
A which is in series with the resistance under test. The cur- 
rent in coil A exerts a deflecting torque toward the position 
shown in Fig. 245, and opposes that produced by coils B and 
B'. As the system moves, the coils B and B' offer an in- 
creasingly strong restraining torque until the turning force 
due to coil A is balanced and the needle comes to rest at a 
point on the calibrated scale which correctly indicates the 
value of the resistance connected between the external ter- 
minals. Should these terminals become short-circuited no 
harm is done to the instrument; the coil A simply overpowers 
coils B and B' and the pointer is moved to the lowest point on 
the scale, marked zero. Both circuits in the instrument have 
suitable series resistances, as indicated in Fig. 245, for the 
purpose of properly protecting the sensitive parts from unduly 
large currents. The voltage produced by the generator in 
these instruments varies from 100 to 1000 volts direct current, 
depending upon the range of the instruments. /'Megger" 
testing sets are adapted to a wide range of measurements, 
such as testing the insulation resistance of motors and genera- 
tors, of house wiring, and of power and telephone cables, 
measuring resistance of conductors, etc. 



, QUESTIONS 

T. How would you measure the resistance of an incandescent lamp 
while illuminated? Give a sketch. 

2. By what method would you measure the cold resistance of the 
lamp in Question 1? 

3. How would you measure the resistance of a coil of wire using a 
voltmeter of known resistance and a source of electric pressure? Give a 
sketch. 

4. With a voltmeter only, and a source of E. M. F., how would you 
measure the insulation resistance of the field windings of a generator? 
Give a sketch. 

5. What is the fundamental principle of the Wheatstone bridge? 
Give a sketch. 



304 LESSONS IN PRACTICAL ELECTRICITY 

6. The highest and lowest resistances available in the rheostat of a 
Wheatstone bridge are 10,000 ohms and 0.1 ohm respectively. The A 
and B arms have each 1-, 10-, and 100-ohm coils. What are the highest 
and lowest resistances that the bridge is capable of measuring? 

7. In making a resistance measurement with a Wheatstone bridge, 
how would you know when too much, or too little, resistance has been 
inserted in the rheostat? 

8. Explain what is meant by a "decade" as applied to resistance 
boxes. 

9. What is the advantage of the decade testing sets over the old type 
testing sets such as the Post -Office bridge? 

10. What are the two general types of ohmmeters? Explain the 
operating principle of each. 

11. Describe the operation of the "Megger." 



PROBLEMS 

1. The drop across the series field coil of a dynamo carrying 250 am- 
peres is 0.7 volt. What is its resistance? Ans. 0.0028 ohm. 

2. A rheostat, battery, galvanometer and unknown resistance are 
joined in series. With 40 ohms unplugged in the rheostat the galvanom- 
eter deflection is 33. The unknown resistance is cut out of circuit and 45 
additional ohms are inserted to reduce the deflection to its former value. 
What is the value of the unknown resistance? Give a sketch. Ans. 45 
ohms. 

3. You are required to measure the insulation resistance of an elec- 
tromagnet using a proportionate deflection galvanometer whose sensi- 
bility is 0.00001 ampere per division. Using a 250-volt supply circuit 
on the electromagnet causes the needle of the galvanometer to be deflected 
3 divisions. What is the insulation resistance? Give a sketch. Ans. 
8,333,333 ohms or 8.3 megohms. 

4. The field magnets of a dynamo having a resistance of 84 ohms are 
connected in series with the field magnets of another machine, and a 
current is sent through the circuit. The drop on the latter field coils is 
111 volts, and on the 84-ohm coils is 37 volts. What is the resistance of 
the second set of field magnets? Ans. 252 ohms. 

5. Balance is obtained in a Wheatstone bridge when A = 10 ohms, 
B = 100 ohms, and rheostat = 14 ohms. What is the value of the un- 
known resistance? Give a sketch. Ans. 140 ohms. 

6. Using a 10-ohm standard resistance with a slide-wire bridge having 
a wire 10 inches long, specify the calibration of the wire so as to indicate 
directly by the position of the slider the resistance of an unknown. 



LESSON XX 

ELECTRICAL DEVELOPMENT OF HEAT 

Heating of Conductors and Their Safe Current-carrjdng Capacity — 
Table XIII — Electrical Development of Heat — Electrical Equiva- 
lent of Heat — Relation Between Heat, Mechanical and Electrical 
Energy— Relation Between Fahrenheit and Centigrade Thermometer 
Scales — Dependence of Resistance upon Temperature — Table XIV 
— Fuses — Electric Welding — Electric Cautery, Blasting, Heating 
and Cooking — Measurement of Temperature by Resistance Change; 
Pyi'ometry — Thermo-electric Pyrometers — Table XV — Questions 
and Problems. 

236. Heating of Conductors and Their Safe Current-carry- 
ing Capacity. — ^Heat is evolved when the molecules of a body 
are set in motion. To produce this motion requires the expen- 
diture of a definite amount of mechanical energy. When a 
current of electricity passes through a wire; a certain amount 
of work is performed in overcoming the resistance of the wire, 
and this work appears as heat, the amount generated agreeing 
with the principle of conservation of energy (^ 144). This 
heating effect becomes very noticeable when the wire is small 
and the current large; the wire may then become so hot that 
it is melted by the current. The increase in the temperature 
of a wire, due to the current, depends upon its weight or sec- 
tional area. For example, two copper wires, one weighing 
one pound, and the other twice as long but weighing four 
pounds, offer equal resistance to a given current passed through 
them, but the wires will not be raised to the same tempera- 
ture, although the amount of heat evolved in both cases is 
exactly the same. This is true because there is more metal 
to heat in one case than in the other. Thin wires, therefore, 
heat much more rapidly than thick ones of a Uke resistance 
when traversed by the same current. Since the resistance of 
metals increases as their temperature rises, a wire will have 
its resistance increased as it becomes heated, and will con- 
tinue to grow warmer until its rate of loss of heat by conduc- 

305 



306 



LESSONS IN PRACTICAL ELECTRICITY 



tion, convection and radiation to the surrounding air or other ob- 
jects equals the rate at which the heat is evolved by the current. 

Experiment 80. — When a chain made of alternate Hnks of platinum 
and silver wire of the same size, is connected to several cells joined in 
series, the platinum links become red-hot but the silver links remain com- 
paratively cool. The resistance of platinum is about 6 times as great as 
silver, but its capacity to absorb heat only about one-half as great, hence 
its rise in temperature is about twelve times as great as that of the silver 
for the same current. 

The heating of a wire by a current is not objectionable 
except that it increases the loss of energy by the rise in resist- 
ance. The real limit of the current-carrying capacity of a 
wire is at such a rise of temperature that the insulation is 
liable to be damaged. The safe current- carrying capacity 
prescribed by the National Electrical Code of the Fire Under- 
writers for copper wires is given in Table XIII. The current- 
carrying capacity is given for both rubber-covered wires and 
for wires having a covering of some other material than rubber. 
It will be noted that the latter wires are permitted to carry 
more current since the insulation covering the wires is not 
as readily affected by the heat as the rubber insulation. 

Table XIII. Current- carrying Capacity of Copper Wires 



B. &S. 

Gage Wire 


Rubber 


Other 


Insulation, 
Amperes 


Insulation, 
Amperes 


18 


3 


5 


16 


6 


10 


14 


15 


20 


12 


20 


25 


10 


25 


30 


8 


35 


50 


6 


50 


70 


5 


55 


80 


4 


70 


90 


3 


80 


100 


2 


90 


125 


1 


100 


150 





125 


200 


00 


150 


225 


000 


175 


275 


0000 


225 


325 



ELECTRICAL DEVELOPMENT OF HEAT 307 

The carrying capacity of copper wires used in dynamos 
varies from 500 to 1000 circular mils per ampere, according 
to the amount of ventilation the wire may receive. A much 
larger allowance must be made for contact surfaces in a circuit, 
as between the brushes of a dynamo and the commutator, the 
chps of a switch, etc.; about 100 amperes per square inch of 
contact surface is an average value. Switches are constructed 
and rated according to their current-carrying capacities. 

237. Electrical Development of Heat. — When an electric 
current flows through a conductor a certain amount of elec- 
trical energy is transformed into, heat energy. This fact may 
be very forcibly illustrated if the current the wire* is carrying 
is great enough to heat it to incandescence. The actual amount 
of heat developed in any case is the exact equivalent of the 
amount of electrical energy expended in overcoming the resist- 
ance of the conductor. The amount of heat developed varies 
directly with the resistance of the wire, the square of the cur- 
rent, and to the time during which the current flows; there- 
fore, if H represents the mmiber of heat units developed, I 
the current in amperes, R the resistance in ohms, and t the 
time in seconds, then the development of heat in an electric 
circuit is given by the following equation: 

H = PxRxt (88). 

where the amount of heat, H, is expressed in joules or watt- 
seconds. These facts were first ascertained by Dr. Joule, and 
the foregoing equation is known as Joule's Law. 

This law may be illustrated as follows: (1) suppose we have 
two equal resistances, A and B, and that twice the P. D. is 
maintained across A that is applied to B, then the heating 
effect in A will be quadruple that in B, since with equal resist- 
ances the current strength will be doubled in A and energy 
is expended four times as fast in A as it is in B. (2) If the 
resistance of B is increased to twice that of A and the same 
P. D. is maintained across both, then the current in B will 
equal one-half that in A. Hence, if in A, H = I^R, then in 
B, H = (|I)2 X 2R = iPR, and consequently twice as much 
heat is developed and twice as much energy expended in A 
as compared with B. (3) If the current in B is then made 



308 



LESSONS IN PRACTICAL ELECTRICITY 



Thermometer 



Calorimeter 



equal to that in A, by doubling the P. D. across B, then in 
A, H = E X I or I2R and in B, H = 2 E X I, or 2 I^R, so that 
doubling the resistance and keeping the current constant 
doubles the heat developed and causes twice the amount of 
energy to be expended. 

238. Electrical Equivalent of Heat. — The amount of heat 
liberated by an electric current may be measured by passing 
the current through a known resistance 
immersed in a known weight of water. 
This is usually done with a device called 
a calorimeter (Fig. 247), which is a vessel 
containing the water in which the resist- 
ance, a coil of platinoid or German silver 
wire, is immersed. The vessel is usually 
double-walled or arranged in some way 
so that it will lose little heat by radia- 
tion into the air. A thermometer is im- 
mersed in the liquid to determine its rise 
of temperature due to the heat given to 
it from the wire. The quantity of heat 
evolved is the product of the mass of 
water and its temperature elevation. 

From a calorimeter experiment made 
by Dr. Joule, to determine the heat equi- 
valent of electricity, he found that one 
ampere flowing through one ohm for one second always de- 
veloped 0.24 of a calorie of heat — a calorie being the amount 
of heat required to raise the temperature of one gram of water 
one degree Centigrade. Therefore, 1 joule of energy is equiva- 

1 




^>^////y>///////////////////9Z 



Fig. 247. — Calorimeter. 



lent to 0.24 calorie of heat or 1 calorie is equivalent to 



0.24 



= 4.2 



joules. These numerical values are known as Joule's 
coefficient or the electrical (or mechanical) • equivalent of heat. 
These values are used when the weight of water is measured 
in grams and the temperature rise is taken with a Centigrade 
thermometer (^240). 

To FIND THE AMOUNT OF HEAT DEVELOPED IN A CON- 
DUCTOR IN calories: 



ELECTRICAL DEVELOPMENT. OF HEAT 309 

Multiply 0.24 times the resistance of the conductor by the square 
of the current and by the time {in seconds) that the current flows, 
as is given by Joule's Law: 

H = 0.24xI2XRxt (89). 

The British Thermal Unit of heat (abbreviation B. T. U.) 
is the amount of heat required to raise one pound of water 
one degree Fahrenheit. Since one ampere flowing for one 
second through one ohm resistance is found to develop 0.000948 
of a B. T. U., this value 0.000948 is the heat equivalent used 
if the weight of water is expressed in pounds and the rise in 
temperature is noted with a Fahrenheit thermometer. 

To FIND THE AMOUNT OF HEAT, EXPRESSED IN B. T. U., 
THAT WOULD BE DEVELOPED IN A GIVEN TIME BY THE 
EXPENDITURE OF . ELECTRICAL ENERGY IN A CIRCUIT: 

Multiply the watts expended by the time (in seconds) that the 
current flows and this product by 0.000948, as in following 
formula : 

H = 0.000948 X E X I X t, (90). 

or H = 0.000948 xP X R Xt (91). 

When it is desired to determine the amount of heat that 
would raise a quantity of water to a certain temperature from 
an initial temperature, multiply the weight of water by the 
degrees rise. If the heat is to be expressed in calories then 
H = grams x degrees Centigrade, and if in B. T. U. then H 
= pounds X degrees Fahrenheit. 

Problem 109. — How many heat units are evolved in one-half hour (1800 
seconds) by a 110-volt incandescent lamp taking a current of ^ ampere? 
By Formula (90) H = 0.000948 X 110, x 0.5 x 1800 = 93.82 B. T. U. 

To FIND THE CURRENT REQUIRED TO PRODUCE ANY GIVEN 
NUMBER OF B. T. U. BY A KNOWN E. M. F. IN A GIVEN 
TIME USE THE FORMULA: 

" 0.000948 X E X t ^^^^* 

To FIND THE TIME REQUIRED * TO PRODUCE A GIVEN 
NUMBER OF B. T. U. BY THE EXPENDITURE OF A GIVEN 
AMOUNT OF ENERGY USE: 



310 LESSONS IN PRACTICAL ELECTRICITY 

t = (93). 

0.000948 X E X I ^ ^ 

These equations result from equation (90) by transposition. 

Problem 110. — A 110-volt, ^-ampere incandescent lamp is immersed 
in a vessel containing 1 pound of water. How long a time will be required 
to raise the water to the boiling point? The temperature of the water 
before the test is 60° F. Neglect the losses due to radiation, etc., and as- 
sume that all the energy is converted into heat. 

The water must be raised 212° - 60° = 152° F. 

The heat units to be given to the water = 1 lb. x 152° = 152 B. T. U. 

152 
By Formula (93) t = 0.000948x110x0.5 ^^^^'^ ^^«°°*> 

or -— - = 48 minutes and 36 seconds. 
bO 

Problem 111. — What current will be required by a lamp immersed 
in the above pound of water to boil it in one-half hour? The E, M. F. 
is 110 volts and the heat losses are to be neglected. 

Solve by Formula (92). Ans. 0.81 ampere. 

239. Relation Between Heat, Mechanical and Electrical 
Energy. — Referring to If 142, Formula (52), etc., we find 
that the electrical work performed in a circuit is proportional 
to the same factors as the heat development. Formulae (88) 
to (90). This is necessarily true, since the electrical work 
expended appears as heat. The following problem will illus- 
trate the relation between electrical work, in joules, and the 
heat, in calories or B. T. U. 

Problem 112. — A current of 4 amperes flows through 2 ohms for 30 
seconds, (a) Find the work performed in joules, (b) Find the number of 
heat units developed in the circuit. 

By Formula (52) J=I2xRxt = 4x4x2x30=960 joules, 

By Formula (89) H = 0.24 I2 x R X t = 0.24 x 960 = 231 calories, 

By Formula (91) H = 0.000948 I^ x R X t = 0.000948 x 960 = 0.910 B. T. U. 

The relation between mechanical energy, electrical energy and 
heat energy (^ 145) is then summarized as follows: 

^ERGY 

u. 



ECHANICAL ENERGY 


ELECTRICAL ENERGY 


HEAT ENERGY 


778 foot-pounds 
3.09 


= 1055 joules = 

4.2 " 


252 calories =1 B. T 
1 calorie 0.00397 


0.737 


■ 1 joule 


0.24 " 0.000948 " 



ELECTRICAL DEVELOPMENT OF HEAT 



311 



240, Relation between Fahrenheit and Centigrade Ther- 
mometer Scales. — Since both the Fahrenheit and Centigrade 
thermometric scales are much used in referring to 
the resistance of a wire at a particular temperature, 
the relation between them is given by the formulae 
below, and also shown diagramatically by Fig. 248. 
On the Fahrenheit scale the melting point of ice is 
placed at 32° and the boiling point at 212°, while 
on the Centigrade scale the melting point of ice is 
placed at zero and the boiling point at 100°. 
Therefore, iOO Centigrade degrees = 212 - 32 = 180 
Fahrenheit degrees, or the ratio of a degree Centi- 
grade to a degree Fahrenheit is as 9 is to 5. In 
converting a Centigrade reading into a Fahrenheit 
reading 32 must be added after multiplying by 
I", and conversely 32 must be subtracted from a 
Fahrenheit reading before multiplying by f. 

To CONVERT A READING FROM THE FAHRENHEIT 

TO THE Centigrade scale: 

Subtract 32, multiply by 5 and divide by 9. 

(F° - 32)5 



Boiling Point 

-100 
200 -jz 

180-^ =_ 

170-f: 

160-^ 
4.150i 
"o 140^ 

IJO-^ 

120-i — 50 D^ 

llO-f 
OlOO-i! 



60^2 



Freezing Point 

Fig. 248.— 
Comparison 
of Fahren- 
h e i t and 
Centigrade 
Thermome- 
ter Scales. 



c° = 



9 



(94). 



To CONVERT A READING FROM THE CeNTIGRADE TO THE 

Fahrenheit scale : 

Multiply by 9, divide by 5 and add 32. 
^o C° X 9 



+ 32 



(95). 



Problem 113. — A field-magnet spool is said to have a resistance of 25 
ohms at 15.5° C. Express this temperature in degrees Fahrenheit. 

15.5 X 9 



By Formula (95) F° = ^-^ + 32 



+ 32 = 59.9, or nearly 



60° F. 

Problem 114. — The temperature of a certain type of insulation should 
not exceed 180° F. What is the corresponding temperature on the Centi- 
grade scale? 

By Formula (94) C = ^^^^^ = (180-32)_><_5 _ ^^^^^ ^^ 



312 LESSONS IN PRACTICAL ELECTRICITY 

241. Dependence of Resistance Upon Temperature. — As 

indicated in ^ 67 on the Laws of Resistance, the resistance of 
all pure metals increases with rising temperature. The pro- 
portional change in resistance of a wire with a unit change in 
temperature is known as the temperature coefficient, or it is the 
amount in ohms that the resistance increases per ohm, for 
each degree rise in temperature. 

The temperature coefficients for the different metals are 
determined experimentally and their value depends upon what 
temperature is taken as the standard or initial temperature. 
Representing the initial temperature by t, the temperature 
coefficient of resistance of copper on the Centigrade scale is 

1 

given by the equation a = 004 f: , ^ J consequently for an ini- 
tial temperature of 0° Centigrade, the resistance of copper in- 
creases = 0.00427 ohm per degree for each ohm at 

234.5 + 

0° C. For example, if the resistance of a copper wire is 10 
ohms at 0° C, for a rise of 1° C. it would have a resistance of 
10 + (10 X 0.00427) or 10.0427 ohms, and at a temperature of 
20° C. it would have a resistance of 10 + (10 X 20 x 0.00427) 
= 10.854 ohms. 

The average temperature coefficient between 0° and 100° C, 
and 32° and 212° F. for all pure metals is roughly the same, 
and is about 0.004 per degree Centigrade and 0.0023 per 
degree Fahrenheit. 

This change in the resistance of a wire due to the temper- 
ature rise or fall is a very important matter in electrical calcu- 
lations and measurements, and must always be taken into 
consideration. The following formulae and temperature coeffi- 
cients, Table XIV, will enable the student to calculate the 
resistance of cliffe^'ent metals at different temperatures: 

Let R = resistance of a conductor at the initial temperature, 
Ri = resistance after a rise or fall in temperature, 
T = number of degrees rise or fall, 
a = the temperature coefficient, or the change of resist- 
ance per degree per ohm. 



ELECTRICAL DEVELOPMENT OF HEAT 



313 



The formula for finding the increase in resistance due to a rise 
in temperature is: 

Ri = R[l + (axT)] (96). 

For a drop in temperature T is taken negative, or the equation 
may be written 

Ri = R [1 _ (a X T)]. 

When the Centigrade scale is used select the temperature 
coefficient (a) for this scale and similarly for the Fahrenheit 
scale. The following temperature coefficients (values of a) 
for some metals represent accepted values for an initial tem- 
perature of 68° F. or 20° C, unless otherwise stated. The 
figures give the amount 1 ohm would increase or decrease in 
resistance when subjected to a rise or fall of one degree F. or C. 



Table XIV. Temperature Coefficients of Resistance 



Metal 



Silver 

Copper (annealed) 

Aluminum 

*Platinum 

Iron 

*Nickel 

Lead 

Nichrome 

German silver (average) 
Manganin 



Fahrenheit 


Centigrade 


Scale 


Scale 


(at 68° F.) 


(at 20° C.) 


0.00210 


000377 


0.00218 


0.00393 


0.0022 


0.0039 


0.00204 


0.00367 


0.00293 


0.00527 


0.0035 


0.0062 


0.00215 


0.00387 


0.00024 


0.00044 


0.00017 


0.00031 


0.00001 


0.00002 



* Average value for range from 0° C. to 100° C, 

Problem 115. — The resistance of the field magnets of a dynamo is 
55 ohms at 70° F. ; after a ten-hour run the temperature indicated by a 
thermometer placed against them is 160''. (a) What is their resistance at 
this temperature? (b) What would be the resistance at 32° F.? 

Since 70° F. = 21.1° C, the temperature coefficient of copper to be 

used in this problem is a = ;;^7t — rr- = k^t-^ = 0.00392 for the Cen- 
tigrade scale or f x 0.00392 = 0.00218 for the Fahrenheit scale. 



314 LESSONS IN PRACTICAL ELECTRICITY 

By Formula (96) for a temperature rise of 160- 70 = 90° F., 
Ri = R [1 + (a X T)] = 55 [1 + (0.00218 x 90)] = 65.8 ohms (a). 

The resistance of the magnets at 32° F. would be Ri = 55 [1 - (0.00218 
X 38)] = 50.4 ohms (b). 

242. Fuses. — When a piece of copper and a piece of lead 
wire of the same size are connected in series and a current of 
increasing strength passed through them, it will be observed 
that the lead will melt when a temperature of 615° F. is at- 
tained, while at that temperature cop- 
per will not melt. Lead containing a 
9i||t.; ijll small percentage of tin will melt at a 
X^Bi'iiii^ T? lower temperature than pure lead, and 
^-^ this alloy is used in electric fuses for 
■K i the protection of the copper conductors. 
A fuse inserted in series with electric 
circuits for their protection consists of 
a wire or strip of lead-tin alloy of such 
a size that it will melt and automati- 

Fig. 249. — Plug Fuses. ^^^^^ ^P^^ ^^^ circuit when the current 

flowing in it exceeds a predetermined 

value. The carrying capacity of a fuse depends upon its cross 

section ; thus commercial fuse wire yo i^^h in diameter will be 

melted by a current of 55 amperes. 

A fuse is generally rated to be of so many amperes capacity, 
meaning that it will carry this current without melting or 
''blowing," as it is termed, and melt on a slight increase in 
current above its capacity. The function of a fuse, therefore, 
is to open the circuit before the temperature rise due to an 
excessive current from any cause, has opportunity to unduly 
heat the conductors. A circuit breaker (Fig. 146) performs 
the same function in a different way. 

Fuses for the protection of electrical apparatus and circuits 
should melt at a definite current value and not be influenced 
by long heating; they should maintain good contact with 
the circuit by having hard metal end connections; they should 
be of sufficient length so that an arc will not be maintained 
when they melt, and should be so arranged that surrounding 
objects are not likely to be set on fire when they melt. Fuses 




ELECTRICAL DEVELOPMENT OF HEAT 



315 



are connected in electric circuits at switch and panel-boards 
or at porcelain blocks provided with metal terminals for hold- 
ing the fuse; the latter device is termed a cut-out, or fuse 
block. The early form of fuse was a lead-tin alloy wire or 
strip provided with copper terminals with which it was held in 
the fuse block; this was known as the open-link fuse; it was 
rather unsafe and unreliable. Modern fuses are completely 
enclosed in a container which is held in the fuse block. One 
form (Fig. 249) , termed a plug fuse, has a screw thread on one 
end and is- screwed into a plug type 
cut-out. The left-hand illustration 
shows a non-refiUable plug fuse, while 
that at the right shows a modern re- 
newable type. The latter has the ad- 
vantage over the older type of plug 
fuse in that when the fuse melts the 
cartridge can be removed from the 
case and a new cartridge fuse inserted ; 
these plug fuses are made for various 
currents up to 30 amperes. 

Cartridge or enclosed fuses consist 
of a fiber tube with a brass cap at 
each end ; the fuse link of lead-tin alloy 
held inside of the cartridge reaches 
from one brass cap to the other, and 
is surrounded by an insulating powder, ^^^^fus?"' Type Fust 
When the fuse ''blows" some of the 

fuse metal is melted and vaporized and an arc tends to form 
across the gap; the powder cools and condenses the vapor so 
that the gap is rendered nonconducting, and the arc is quickly 
extinguished. For cartridge fuses up to 60 amperes, shown at 
the left of Fig. 250, contact is made with the circuit by chps 
which grip the end caps, and for larger sizes, the knife blade 
contact is used, show^n at the right in Fig. 250. Most cartridge 
fuses are equipped with some sort of indicator so that upon 
external inspection one can determine if the fuse is in good con- 
dition OT has been blown. Several manufacturers make enclosed 
fuses which permit of the renewal of the fusible element, thus en- 
abling the cost of fuse maintenance to be materially lessened. 




Fig. 250. 



316 



LESSONS IN PRACTICAL ELECTRICITY 



243. Electric Welding. — Metals and alloys can be welded 
with the aid of the electric current, two distinct processes being 
employed, namely: the so-called incandescent process, and the 
arc process. The principle of the incandescent welding process, 
devised by Elihu Thomson, is that of causing a current of 
electricity to pass through the relatively high resistance pre- 
sented at the junction of two 
metals, thereby generating 
heat. The two general 
methods of making an elec- 
tric weld by the Thomson 
process are the butt weld and 
the spot weld. In the butt 
weld a current of electricity 
is passed through the abut- 
ting ends of the pieces of 
metal that are to be welded, 
thereby generating heat at 
the point of contact, which is 
also the point of greatest re- 
sistance, while at the same 
time mechanical pressure is 
applied to force the parts 
together. The passage of 
current through the metal at 

the point of junction gradu- 
Fig. 251. -Winfield Spot-welder. ^jjy ^^^ ^^-^^^ ^^^^^^ ^j^^ 

temperature of the metal to the welding point, and the mechani- 
cal pressure applied simultaneously affects the weld. In the 
spot weld two or more metal sheets or parts are fused together 
electrically between two electrodes or welding points which are 
brought to bear on the plates where it is desired to make the 
weld. The metal parts to be welded are poor conductors of 
electricity relative to the electrodes and, therefore, offer so great 
a resistance to the flow of current that the metals heat almost 
to the molten state, and then, by applying pressure on the elec- 
trodes, the metals are forced together and the weld effected. 
The weld thus produced is mechanically equivalent to riveting, 
but it is stronger and can be done much more quickly and 
economically. 




ELECTRICAL DEVELOPMENT OF HEAT 317 

Welding machines for electrically welding metals are con- 
structed in a variety of forms and are equipped with water- 
cooled electrodes and with transformers, 1j 357. The transformer 
is made a part of the machine because alternating current is 
generally used; its function being to reduce the commercial volt- 
ages to a low value, since welds are made with heavy currents 
under a few volts pressure. Fig. 251 shows a spot- welder made 
by the Winfield Electric Welding Machine • Company. The 
water-cooled electrodes are shown at the top of the machine, 
the upper one can be pressed against the lower stationary elec- 
trode by means of the foot treadle. The transformer is located 
in the perforated case in front of which is mounted the current 
regulator; this varies the current strength by altering the num- 
ber of turns on the high-tension winding of the transformer. 

In the arc process of electric welding the heat of the arc is- 
utiUzed in bringing the metals to be welded to the proper tem- 
perature. The parts to be joined are connected to one ter- 
minal of the supply circuit and a welding pencil or rod of 
proper composition to the other terminal. Sometimes this 
pencil is not connected to the circuit and a carbon electrode 
takes its place. The welding pencil (diameter | to i^ inch) 
is melted by the arc and fills up the space purposely left be- 
tween the pieces to be welded, this space being formed by 
beveling the edges of the welded parts either on one or on both 
sides. The arc process is much used in the welding of the 
mild steel plates of ship hulls. For plates from J to 1 inch 
thick currents of from 150 to 400 amperes are usually used. 
The Welding Committee of the Emergency Fleet Corporation 
specified that the iron electrode wire for the welding of mild 
steel may have certain impurities to a percentage not in excess 
of the following values: carbon 0.18, manganese 0.55, phos- 
phorus 0.05, sulphur 0.05 and silicon 0.08. Alternating as 
well as direct current may be used for metal arc welding. A 
representative rate of deposit for a good welder with " Quasi- 
Arc " electrodes is about 2 pounds per hour for J-inch plates ; 
this would be about 3 feet per hour with butt joints at 60 
degrees and a free distance of | inch. 

An interesting experiment in electric welding makes use of 
a direct current at 200 volts and requires a metalUc tank con- 



318 



LESSONS IN PRACTICAL ELECTRICITY 




Fig. 252. — Hoskins 
Electric Furnace. 



taining, for example, a solution of ordinary washing soda, the 
solution being connected to the positive pole of the supply 
source. The tongs are connected to the negative pole and the 
piece to be heated is clamped in them and immersed in the 
solution. The specimen soon becomes heated ' to a welding 
heat due to the film of hydrogen which 
collects around the negative pole (by 
electrolysis, 1[ 80) and greatly increases 
the resistance at that point. In welding, 
two pairs of tongs connected to the nega- 
tive pole may be used simultaneously. ; 
244. Electric Cautery, Blasting, Heat- 
ing and Cooking. — In surgery a thin 
platinum wire heated to a white heat by 
the current is used for many operations 
instead of a knife. Platinum is chosen 
because it is the most refractory metal; 
but even this is readily fused when the current is too strong. 

In blasting the fuse is sur- 
rounded by some combus- 
tible material in proximity 
to the explosive. A current 
sent from a distant battery, 
through copper wires, melts 
the fuse or heats the plati- 
num wire, as the case may 
be, and the combustible is 
ignited and the powder ex- 
ploded. 

The heating effect of the 
electric current is also util- 
ized in electric furnaces of 
various sorts for carrying 
on a number of industrial 
tests and processes. Fig. 
252 shows a Hoskins electric 
furnace of the tube-chamber design and also a nickel-chromium 
resistance or heating element. The furnace is designed so 
that the heating elements can be replaced quickly in case 




Fig. 253. — Heating Element of 
Electric Grill. 



ELECTRICAL DEVELOPMENT OF HEAT 



319 





Disk Stove. 



some are damaged. The crucible- and muffle-chamber designs of 

furnace are also much used in chemical and metallurgical work. 

Very large furnaces of various types are 

used for melting and refining steel. A 

10-ton Heroult arc furnace served by a 

3000-kw., 25-cycle transformer requires 

electrical energy to produce steel at a rate 

of about 600 kw.-hrs. per ton. 

In electric cooking utensils, the heating 

element of ^^§-254. 
non-oxidizing alloy may be either 
open or enclosed, and may be 
formed of a flat ribbon wound 
on sheet mica or of a round wire 
wound into a coil and supported 
in mica. An open-coil heating 
element used in a well-known 
electric grill is shown in Fig. 253. 
In the electric disk stove (Fig. 
254) the heating element is en- 
closed. Another useful electric 
heating appliance, the electric 
iron, is shown in Fig. 255, the 
heating element shown in the 
Fig. 255. — Electric Iron and lower part of the figure being a 
ea ing emen . ^^^ metal ribbon wound on sheet 

mica and enclosed within 

the iron shell. Fig. 256 

shows the heating cham- 
ber of electric percolators, 

samovars, etc., in which A 

is the heating element 

mounted on and between 

mica, and B is a safety 

fuse. This fuse is a piece 

of lead secured to the fuse 

plug, and the plug is in- ^ig. 256. — Heating Chamber of 

, 1 • .1 1 • x ercoiatjors. 

serted m the appliance, 

the lead strip is in contact with the two connecting ears shown 




320 



LESSONS IN PRACTICAL ELECTRICITY 



above B and thus closes the circuit. This safety fuse used in 
appliances for heating liquids is melted by the heat in the heat- 
ing chamber and not by the current flowing through it as is the 

case with fuses used for the 
protection of electric cir- 
cuits ( If 242) . If the liquid 
should boil dry while the 
current is on, the piece of 
lead will melt and automati- 
cally open the circuit, pre- 
venting the possibihty of an 
overheated element and con- 
sequent harm to the appli- 
ance. An electric range and 
oven made b}^ the Simplex 
Electric Heating Co. is illus- 
trated in Fig. 257, in which 
the elements are of the en- 
closed type. 

T^- or^T 1-1 X • r^ An electric heating pad, 

Fig. 257. — Electric Oven. i • i ^ i ^i i i- 

which takes the place of a 

hot-water bottle, is useful in many cases of illness. One type, 
the '^ Universal" heating pad, made by Landers, Frary & Clark 
Co., consists of a 
long flexible coil 
of high resistance 
wire enclosed in a 
pad made of as- 
bestos, the pad be- 
ing quite flexible. 
The heating pad 
has three degrees 
of heat, as follows 




Position of element 
wfien heated—^ 




Mica 



Fig. 258. 



Adjustment Screw-' 
Thermostat of the "Universal" 
Heating Pad. 



low, medium and high, these being con- 
trolled at win by the user. In series with the heating coil are 
four thermostats that are also enclosed inside the pad, their 
function being to open the heating coil circuit when the pad 
reaches a predetermined temperature and prevent any possi- 
bihty of overheating. The thermostats, which are in series 
with the heating coil, are placed in circuit by the control 



ELECTRICAL DEVELOPMENT OF HEAT 321 

switch according to the degree of heat desired: a thermostat 
set for a temperature of 125° F. being in circuit on the low 
point of control, one set for 160° F., being in circuit on the 
medium point and two thermostats, each set for 195° F., being 
in circuit on the high temperature point. The construction of 
one of these thermostats is shown in Fig. 258; it consists of a 
metal strip bent in the shape of a hair pin and composed of 
two different metals, A and B, of which A will expand more 
rapidly than B upon an increase of temperature. One end of 
the strip is, held securely while the other end is free to move. 
In Fig. 258, the free end is shown resting on a platinum-tipped 
adjusting screw and thereby closing the circuit, the dotted hues 
in the figure show the position of the free end of the thermostat 
element when it expands due to the temperature reaching the 
value for which it is set to open the circuit. 

245. Measurement of Temperature by Resistance Change 
— Pyrometry. — It was pointed out in H 241 that the resist- 
ance of a metallic conductor depended upon its temperature, 
increasing as the temperature increases. The manner in which 
the change of resistance takes place was indicated by Equation 

(96), viz: Ri = R[1 + (a x T)], 

where R is the resistance at the initial temperature, Ri is the 
resistance at a temperature T degrees higher, and a is the 
temperature coefficient of resistance (or the resistance change 
per ohm per degree) . If R and Ri be measured for a particular 
metal whose coefficient a is known, it is possible to obtain the 
only other unknown factor in the equation, namely the tem- 
perature rise T. Thus, by transposition. Formula (96) becomes 

^'-^ . (97). 



a\R / 



a X R 



Consequently, temperatures may be measured by observing 
the resistances of a coil of wire at those temperatures. This 
method of temperature measurement is sensitive and may be 
employed over the range from the lowest temperatures to over 
1200° C. by utilizing an appropriate material (usually plati- 
num) for the resistance coil. The measurement of high tem- 
peratures is spoken of as pyrometry. 



322 



LESSONS IN PRACTICAL ELECTRICITY 



In order to eliminate the resistance of the wires leading from 
the coil to the resistance measuring instrument, a third wire 
is frequently connected to the coil as shown in Fig. 259, which 
illustrates a Wheatstone bridge for the measurement of resist- 
ance. Herein A and B are the ratio or bridge arms, C is the 
rheostat arm, and the resistance coil P forms the fourth arm 
of the bridge. The connecting cord between the coil P and 

the bridge may be of any 
convenient length and is 
formed of the three num- 
bered wires. It will be 
noted that wires 1-2 and 
2-3 are in the C arm and 
wires 2-3 and 4-5 are in 
the P arm; consequently, 
by making the wires 
exactly of the same size, 
the resistance of the leads 
is eliminated. Then the 
resistance of coil P is 
given by the relation (see 
11232), P = (AxC)^B. 
For convenience, an ohmmeter ( If 235) or a differential 
galvanometer may be used as the resistance measuring device, 
their scales being graduated directly in degrees C. or F. The 
Leeds & Northrup Co. makes a resistance thermometer, 
utilizing a coil of nickel wire, particularly adapted for measur- 
ing the internal temperatures of electrical machinery, the in- 
dicating instrument being virtually a differential millivoltmeter. 
246. Thermo-electric Pyrometers. — Another electrical 
method of measuring temperature is widely used; it utilizes 
a thermo-couple. If an electric circuit is formed of two dissimi- 
lar metals and one junction of those metals is subjected to 
a higher temperature than the other, a current is produced in 
that circuit due to the development of contact electromotive 
forces at the junctions. Over certain ranges of temperature, 
the strength of the current produced by such a thermo-couple 
is found to be proportional to the difference of the tempera- 
tures. Consequently, by keeping one junction at constant 




259. — Three-lead Resistance 
Thermometer. 



ELECTRICAL DEVELOPMENT OF HEAT 



323 



temperature and subjecting the other to the temperature under 
measurement, the latter temperature may be determined by 
observing the current produced. 

A variety of metals are used to form thermo-couples, and are 
broadly classed as rare-metal and base-metal couples. Of the 
former about the most satisfactory couple is that of Le Chatelier, 
which has one element of platinum and the other of an alloy 
of 90% platinum and 10% rhodium; of the latter the copper- 
constant an couple is frequently used for the range from 500° C. 
to the lowest temperatures. The following table shows the 
electromotive forces available with these junctions at various 
standard temperatures, the cold junction being kept at 0° C. 



Table XV. Temperature Millivolt Relations of Thermo-couples 

Millivolts 

Copper- 

Constantan 

Couple 

4.276 

10.248 

11.009 

15.203 

16.083 









E. M. F. in 


Point 


Degree 


Degrees 


Le Chatelier 
Couple 




Centigrade 


Fahrenheit 


Water b.p. 


100 


212 


0.643 


Naphthalene b.p. 


217.9 


427.8 


L585 


<y^m m.p. 


231.9 


449.0 


1.706 


Benzophenone b.p 


305.9 


582.6 


2.365 


•^ Cadmium m.p. 


320.9 


609.6 


2.503 


*^ Zinc m.p. 


419.4 


786.9 


3.430 


Sulphur b.p. 


444.5 


920.1 


3.672 


Antimony m.p. 


630.0 


1166 


5.530 


Aluminum m.p. 


658.7 


1217.6 


5.827 


Silver m.p. 


960.2 


1760.3 


9.111 


Gold m.p. 


1082.6 


1944.6 


10.296 


Copper m.p. 


1082.8 


1981.0 


10.534 


Li2 Si O3 m.p. 


1201 


2193.8 


11.941 


Diopside m.p. 


1391.5 


2536.7 


14.230 


Nickel m.p. 


1452.6 


2646.6 


14.973 


Palladium m.p. 


1549.5 


2821.1 


16.144 


Platinum m.p. 


1755 


3191 


18.608 



The construction of two forms of base-metal thermo-couples 
is shown in Fig. 260. At the top are shown two dissimilar 
wires about one-tenth inch in diameter twisted together at one 
end and welded; the wires themselves are insulated from each 
other by porcelain beads. The lower illustration shows the 
inner metal rod welded to the outer tube and also the insula- 



324 



LESSONS IN PRACTICAL ELECTRICITY 



tion between them. The thermal junction may be placed in 
a furnace or in molten metals for ascertaining their 
temperatures, but they must be protected from fur- 
nace gases or from direct contact with those hquids. 
The external appearance of the hot junction or^re 
rod together with a thermos-bottle cold-junction 
device is shown in Fig. 261, which depicts a plati- 




ij IIHIIIIIIIII II |l4nilllll|UMII|lllll|l| 'II 




Fig. 260. — Construction of Thermo-couple. 

num couple for use in molten brass. This 
couple, made b}^ the Pyrolectric Instrument Co„p 
is insulated by two-hole insulators, and these in 
turn are enclosed in quartz; this quartz tube is 
enclosed with a nichrome tube and over this is a 
sectional graphite protection tube. The instru- 
ment for measuring the current (or E. M. F.) has ^. 
its scale graduated in degrees. Pyi?o meter 

Therm o - 
QUESTIONS couple. 

1. A cell is short-circuited by a thick piece of copper having a low- 
resistance as compared with that of the ceU. Where wall the most heat be 
developed? 

2. Cite an experiment to prove that heat developed in a circuit is 
proportional to the square of the current. 

3. Equal lengths of No. 10 and No. 20 B. & S. gage copper wdre are 
connected in series and to a generator. Is there any difference in the 
strength of current through, or heat evolved from, the two wdres? 

4. A thermometer is immersed in a vessel containing dilute sulphuric 
acid and a plate of zinc and of copper. When the extremities of the plates 
are connected by a wire the temperature rises. Explain this. 

5. The size of wdre for carrying 62 amperes is calculated by voltage drop 
to be, in a certain instance, No. 6 B. & S. Would you use a rubber in- 
sulated wire of this size? Why? 

6. Explain the method of temperature measurement by means of re- 
sistance change. 



ELECTRICAL DEVELOPMENT OF HEAT 325 



PROBLEMS 

1. How many heat units are evolved in 10 hours from an arc lamp 
requiring 10 amperes and 45 volts? - Ans. 15,352 B. T. U. 

2. How many pounds of water can be raised from 80° F. to the boihng 
point by the heat evolved in Problem 1, neglecting all losses? Ans. 116.3 
lbs. 

3. With an E. M. F. of 110 volts what current must be passed through 
a coU of iron wire, immersed in 2 pounds of water so that it will boil in 
45 minutes? The temperature of the water at the start is 60° F. Ans. 
1.08 amperes. 

4. The hot resistance of an electrical laundry iron is 22 ohms and it 
is connected across 110-volt mains. Suppose the iron to be placed into 
a vessel containing 4 pounds of water, the temperature of which is 60° F., 
and the current turned on for 15 minutes. What wdll be the temperature 
of the water at the end of that time, not deducting losses for radiation, etc.? 
Ans. 116.2° F. 

5. Give the equivalent amount of energy in joules and foot-pounds ex- 
pended in the arc lamp in Question 1. Ans. 16,200,000 joules; 11,950,000 
ft.-lbs. 

6. The length of the Institute's concentric power cable, laid in ducts 
under Broad street, is 300 feet, and the size of the conductor is No. 4 
B. & S. gage. Suppose that the temperature in the ducts on a warm 
summer day is 104° F., and on a winter day is 10° F. (a) What will be the 
resistance of the cable in each case? (b) If the cable is delivering 30 kw. 
at 1100 volts, what will be the lost power on the line at the summer tem- 
perature as above? (c) What will be the cost of this loss when operating 
5 hours a day for 6 months (180 days) with energy costing 7| cents per 
horse-power-hour? Ans. (a) 0.165 ohm at 104° F., 0.130 ohm -at 10° F.; 
(b) 123.3 watts; (c) $11.17. 

7. A nickel coil of a resistance thermometer has 5 ohms resistance at 
0° C. At some other temperature its resistance is 7.48 ohr^s. What is 
that temperature if nickel has an average temperature coefficient of 0.0062 
per Centigrade degree? Ans. 80° C. 



LESSON XXI 

ELECTROMAGNETIC INDUCTION 

Electromagnetic Induction — E. M. F. Induced in a Wire by a Magnet — 
To Find the Direction of the Induced E. M. F. — Value of the Induced 
E. M. F. — Lenz's Law of Induced Currents — Currents Induced by 
Electromagnetism — Table XVI — Variation of Induced E. M. F. 
with the Rate of Change of Magnetic Lines of Force — Eddy Currents 
— Magnetic Hysteresis — Mutual Induction — Self-induction — In- 
ductance — Reactance and Impedance — Neutralizing the Effects of 
Self-induction — Questions. 

247. Electromagnetic Induction. — In Lesson XIII a cur- 
rent of electricity flowing through a wire was found to set 
up around the wire a magnetic iield (Fig. 125). If a wire is 
arranged so as to form a closed circuit and then moved across 
a magnetic field so that it will cut the magnetic flux, a current 
of electricity is produced in the wire; in other words, if we 
artificially produce around the wire the magnetic flux, a cur- 
rent of electricity flows through it when the circuit is com- 
plete. The English physicist, Michael Faraday, discovered 
(in 1831) that electric currents could be produced in a closed 
circuit by moving magnets near it, or by moving the circuit 
across a magnetic field. In order to have an electric current 
flow through a circuit there must be an E. M. F., therefore, 
when a wire is made to cut magnetic flux, there is first set up 
at the terminals of that wire an induced E. M. F., and when 
the circuit is completed, a current will flow in consequence of 
this induced E. M. F. Currents that are so generated are 
known as induction currents and the phenomenon termed elec- 
tromagnetic induction. This is a most interesting and valuable 
branch of the study of electricity, as upon its * principles is 
based the operation of many forms of commercial electrical 
apparatus, such as dynamos, transformers, induction coils, 
etc. Electromagnetic induction should not be confused with 
magnetic induction (If 21). 

326 



ELECTROMAGNETIC INDUCTION 



327 






248. E. M. F. Induced in a Wire by a Magnet. — Consider 
a copper wire connected to a sensitive galvanometer, G 
(Fig. 262), and so located that a portion AB is within the in- 
fluence of the bar magnet NS. If the wire AB is quickly moved 
down past the pole of the magnet a moinentary current will flow 
in the wire due to the induced E. M. F., causing the galva- 
nometer needle to be deflected, say to the right of zero, after 
which it will again return to the zero position. If the wire is 
again moved up past the same pole 
another momentary current will flow 
in the wire in the opposite direction 
to the former current, as indicated 
by the momentary deflection of the 
galvanometer needle which now 
swings to the left of zero. If the 
induced current, then, flows from 
B to A on the downward motion it 
will flow from A and B on the up- 
ward motion. If the wire be moved 
rapidly up and down past the mag- 
net, the current will alternate in 
direction with each direction of 
motion, or an alternating current 
(Tf 339) will flow in the wire. When this motion is rapid, and 
consequently the alternations rapid, the needle does not have 
sufficient time to take up the respective positions due to the 
opposite currents traversing the instrument and will remain at 
zero, appreciably vibrating, however. 

(1) If the wire is held stationary and the magnet moved, the 
same results are noted. 

(2) // the 'opposite pole of the magnet is used, the direction of 
the induced E. M. F. and of the current in each instance is oppo- 
site to what it was before. 

(3) An electromagnet used instead of the permanent bar mag- 
net will produce the same results. 

(4) The current in the circuit does not weaken the magnet, but 
is produced by the expenditure of muscular energy, just as in a 
cell the current is produced by the expenditure of chemical energy. 

(5) The momentary induced E, M, F, is greatest when the 




Fig. 262. — Current Es- 
tablished in a Wire by Mov- 
ing It near a Magnet. 



328 



LESSONS IN PRACTICAL ELECTRICITY 



wire is moved so as to cut the magnetic lines of force at right 
angles. 

(6) // the wire in Fig. 262 does not form a closed circuit an 
E. M. F. will still he induced in the wire when motion occurs and 

be available at its terminals, just as 
an E. M. F. exists at the terminals of 
a cell on open circuit tending to cause 
a current to flow (^ 35). 

249. To Find the Direction of the 
Induced E. M. F. — Right-hand 
Rule. Place the thumb, the first and 
second fingers of the right hand all at 
right angles to each other {Fig. 263) 
and in such relation to the wire that 
the first finger points in the direction 
of the magnetic fiux of the magnet, 
'and the thumb in the direction of mo- 
tion of a wire-; the second finger will then indicate the direction 

OF THE INDUCED E. M. F. IN THAT WIRE. 

Applying this rule to the wire AB of Fig. 264, which is being 
moved down past the N-pole of the mag- 
net, we find that the direction of cur- 
rent is frojn B toward A. If either the 
polarity or direction of motion be re- 
versed, the current in the wire AB will 
be reversed, as can be proved by this 
rule. If both the polarity and motion 
are reversed the current will be in the 
same direction as in the figure. The 




- Right-hand 
Rule for Determining the 
Direction of Induced E.M.F. 



Lines of Force 




Fig. 264. — Application 
of Right-hand Rule. 



student should prove these statements by the above rule. 



Another method of ascertaining the direction of the induced current 
recalls to mind the direction of the magnetic whirls around a wire which 
corresponds to the direction of current through it (Fig. 125). If the wire 
AB (Fig. 264) is moved downward across the lines of force which extend 
from left to right, the direction of motion is such that if the magnetic lines 
below the wire were flexible they would tend to wrap themselves around 
the conductor in an anti-clockwise direction, and if the wire is grasped 
with the right hand so that the fingers will show the direction in which 
the magnetic lines are wrapped around the wire, the extended thumb will 
indicate the direction of current. Since the tendency of the induction is, 



ELECTROMAGNETIC INDUCTION 



329 



in this case, to produce magnetic whirls in a direction which is anti-clock- 
vjise as you look along the wire, the current set up will flow toward you, 
or from B toward A. 

250. Value of the Induced E. M. F. — The magnitude of 
the induced E. M. F. generated in a conductor when it is cut- 
ting lines of force is proportional to 
''the rate at which the hues of force are 
cut. When a conductor cuts lines of 
force at the rate of 100,000,000 per 
second, a pressure of one volt is set up 
between its terminals. 

If a single conductor is moved 
across a magnetic field, the average 
number of hues of force cut per second 
by the conductor would equal the 
total number of lines of force con- 
tained in the field, divided by the 

time in seconds required to move- the -rr- o«r t • ^u 

;^ Iig. 265. — Increasmg the 

conductor across that held, ihenum- Induced E.M.F. by Increas- 

ber of fines of force cut by a wire in ing the Number of Cutting 

one second moving in a magnetic field, ^^^** 

therefore, depends upon the strength of the field and the speed 

at which the wire is 
moved. The number of 
lines cut will also depend 
upon the length of the 
wire, and upon the angle 
at which the wire moves 
across the field (1[ 253). 
If a wire, AB of Fig. 265, 
cuts a certain number of 
hnes of force per second, 
causing a pressure of one 
Polarity volt to be set up between 
Current its ends, and there are 



CoilofWlre. 



Motion of Magnet 




Fig. 266. 
Produced in 



- The Magnetic 

the Coil by the 
tends to Stop the Motion Producing the +v,T,pp ci^iln^ wiVp^ ioinpd 
Current — Lenz's Law. }^^^^ SimUar wires j omed 

m series and moved so as 
to cut the same number of hnes per second as the single wire, 
three times the pressure would be set up, namely three volts. 



330 LESSONS IN PRACTICAL ELECTRICITY 

The induced E. M. F. will, therefore, depend upon the 
following factors: 

(a) The strength of the magnetic field {the number of lines 
of force that it contains); 

(b) The speed of the wire in cutting the flux; 

(c) The number of wires cutting the lines of force. 

To increase the E. M. F. induced in a wire, it may be coiled 
up to form a solenoid (Fig. 266) and connected to the galva- 
nometer. If a permanent magnet or an electromagnet be thrust 
into the solenoid, a momentary induced current will flow 
through the galvanometer according to the conditions given 
in 11248. 

Experiment 81. — Connect the student's galvanometer (Fig. 172) to 
the "secondary coil" (Fig. 266) and using a bar magnet make experiments 
to verify all the statements given in \\ 248. 

Experiment 82. — With two bar magnets held together to make a 
compound magnet, prove statements (a) and (b) above. 

Experiment 83. — To prove statement (c) above, substitute for the 
coil used in Experiment 81 a solenoid containing a different number of 
turns of wire. 

Experiment 84. — Connect a cell to the detector galvanometer (Fig. 
172) and note whether the needle is deflected to the right or left of zero 
when the current enters by the right-hand binding post. Having deter- 
mined the direction of deflection for a particular direction of current 
through the instrument, substitute for the cell the secondary coil, and 
repeat the experiments enumerated in H 248. Find the direction of the 
current in the coil by tracing the direction of the winding, noting the 
direction of deflection of the galvanometer needle and applying the right- 
hand rule. 

251. Lenz*s Law of Induced Currents. — If Experiment 84 
be carefully performed it will be found that as one pole of a 
magnet is thrust toward the coil, the direction of the current 
caused by the induced E. M. F. will be such as to make the 
face of the coil near to the magnet's pole of the same polarity 
as that pole (Fig. 266). Hence, there is a magnetic repulsion 
between the magnet and the coil when one is being approached 
to the other. When the magnet's pole is withdrawn the direc- 
tion of the induced current is reversed; the face near the magnet 
will now have opposite polarity to the pole of the magnet, and 
consequently attraction exists between them. In each instance 
the magnetic attractions or repulsions tend to oppose the motion 



ELECTROMAGNETIC INDUCTION 331 

of the magnet. The above statements are expressed concisely in 
Lenz's Law^ as follows: 

In all cases of electromagnetic induction the direc- 
tion OF the current occasioned by the induced E. M. F. 

IS SUCH THAT THE MAGNETIC FIELD SET UP BY IT TENDS TO 

STOP THE MOTION PRODUCING IT. To produce the current in 
the coil energy must be expended in bringing the magnet to 
the coil and in taking it away. If the magnet is moved by 
hand, muscular energy is expended; if attached to the end of the 
piston rod of a steam engine and moved in and out of the coil, 
mechanical energy is expended, and a constant but alternating 
E. M. F. will be produced. It will also be seen that if the coil 
terminals are open or disconnected very little energy will be re- 
quired to move the magnet, since there will only be an induced 
E. M. F. set up, and with no current flowing there will be no 
attractions and repulsions to overcome. 

The extra energy required when the coil is closed is expended 
in producing the current, and it is in this way that mechanical 
energy is converted into electrical energy in the -electric generator. 
It will be further noted that with a given rate of motion the 
alternating E. M. F. will be constant, and, since the resistance 
of the coil is constant, the current will also be constant. Sup- 
pose a galvanometer of much lower resistance is connected to 
the coil (Fig. 266). The current will now be greater, since 
the resistance is decreased, and, consequently, the power in 
watts will be greater, P = E x I, so that more energy must 
be expended in producing the E. M. F. than before, because 
the magnetic field of the coil to be overcome has been increased 
by the increase of current strength. When lamps are added in 
parallel to the circuit of a generator the resistance of the external 
circuit is lowered, Formula (30) , therefore the E. M. F. causes 
more current to flow through the lower resistance and more me- 
chanical energy must be expended in order to furnish the addi- 
tional electrical energy. 

The word primary is often used as an abbreviation for pri- 
mary coil. The primary coil is the coil producing the induction, 
or it is the inducing body, while the secondary coil, or second- 
ary, is the body under induction. In Fig. 266 the bar magnet 
is the primary body and the coil is the secondary body. 



332 



LESSONS IN PRACTICAL ELECTRICITY 



Seconda 



Primary 




Fig. 267. — The Magnetic 
Polarity Produced in Coil B by 
the Current Set up in it Tends 
to Stop the Motion Producing 
this Current — Lenz's Law. 



Lenz's Law is further illustrated in Fig. 267, where the pri- 
mary body, A, is an electromagnet with its polarity as indicated. 

On moving this electromagnet 
toward the secondary coil, B, the 
induced current flows so as to 
make the near face of B of N- 
polarity, and repulsion results as 
before. During the recession of 
the primary from the secondary 
coil the polarity of the secondary 
is reversed and attraction exists, 
opposing their separation. -The 
attractions and repulsions take 
place only while the coil is mov- 
ing. If the coil stops the current 
in the secondary also stops even 
though the current is maintained in the primary coil. 

252. Currents Induced by Electromagnetism. — Induced 
electromotive for-ce is produced when- 
ever a conductor is cut by magnetic 
lines of force, no matter how this 
cutting may be accomplished. A per- 
manent magnet may be used to pro- 
duce the magnetic field, and either the 
wire or the magnet may be moved to 
induce the ,E. M. F. Again, the mag- 
netic field of a wire carrying a current 
or of an electromagnet may be utilized 
to produce the induction. Mutual in- 
duction and self-induction are also 
examples of electromagnetic induction 
(see II Tl 256 and 257 respectively) . 

Momentary induction currents may 
be demonstrated with the induction 
coil (Fig. 268), which consists of a 
primary and a secondary coil of copper 
wire. An electromotive force will be induced in the secondary 
winding : 

when the primary circuit is closed as shown. 



Primary.. 




268. — Experimental 
Induction Coil. 



ELECTROMAGNETIC INDUCTION 



333 



1. by moving either the primary or secondary circuit; 

when both coils are stationary and one surrounds the other^ 

2. by making or breaking the primary circuit, 

3. by altering the strength of the current in the primary circuit, 

4. by rapidly reversing the direction of the current in the pri- 
mary circuit, 

5. by moving the iron core when a current is flowing through 
the primary circuit. 

A momentary induced current which flows in the opposite 
direction to that of the current producing it, is sometimes 
spoken of as an inverse current, and one which flows in the 
same direction, a dired cur- 
rent. The above methods -— /\^ 
for producing induction ^—^ 

are treated in the follow- 
ing paragraphs. 

First Method: Moving 
Either the Primary or Sec- 
ondary Circuit. — ■ When 
either the primary or sec- 
ondary circuit is moved 
relatively to the other the 
results are the same as 
those given for a perma- 
nent magnet ( ^ 248) , and 
should be verified by the apparatus shown in Fig. 268. The 
principle involved may be further illustrated by considering the 
coils to be stretched out as shown in Fig. 269 at AB and CD. 
With the key closed in the primary circuit CD magnetic whirls 
surround the wire, and if the secondary wire AB is moved toward 
CD, it cuts the lines of force of the primary circuit, producing 
a momentary current during the motion. The direction of 
this induced current is opposed to that of the primary current 
as indicated ; it is an inverse current. Verify this statement 
by the right-hand rule of If 249. If the secondary be moved 
away from the primary, the secondary circuit is again cut by 
the primary flux, and a direct momentary current is induced. 

Second Method: Making or Breaking the Primary Circuit. 
— Consider both circuits stationary in Fig. 269. At the 




Fig. 269. — Inverse Secondary Current 
on Approaching Primary. 



334 



LESSONS IN PRACTICAL ELECTRICITY 



instarit the switch is closed the magnetic Hnes of force spring- 
ing from the primary circuit CD cut the secondary circuit AB, 
and an inverse momentary current flows through the second- 
ary, for the period of time required to establish the field around 
the primary. When the switch is opened the magnetic lines of 
the primary will collapse upon it and again cut the second- 
ary, but in the opposite direction, producing a direct current. 
These results are summarized in Fig. 270. If the primary 
switch be automatically closed and opened, the momentary 
induced currents will become regular and will change their 
direction with each make and break of the primary. Whether 




Make" of Primary Circuit "Break" of Primary Circuit 



Fig. 270. 



- Induced Current in Secondary on the "Make" 
and "Break" of the Primary Circuit. 



the conductor is wound into rectangular or into cylindrical 
coils, the same principles apply. The induction coil ( \\ 263) 
is constructed on this principle. 

Third Method: Altering the Strength of the Primary Cur- 
rent. — • If a rheostat is introduced into the primary circuit 
the current can be altered without breaking the circuit. When 
the resistance is decreased a momentary inverse current is 
induced in the secondary circuit, since the magnetic lines of 
the primary at the instant of change in resistance become 
greater than before, or spring outward. With an increase in 
resistance the primary Hnes cut the secondary in the opposite 
direction as they collapse toward the primary wire, and a direct 
momentary current is induced. 

Fourth Method: Reversing the Direction of the Primary 
Current. — A switch arranged to automatically reverse the 
current in the primary many times per second would produce 



ELECTROMAGNETIC INDUCTION 



335 



therein an alternating current, the magnetic whirls of which 
would- be continually rising, falling, and changing their direc- 
tion with each reversal. A secondary wire brought into the 
vicinity of a wire carrying such a current would be continually 
cut by the varying magnetic lines of force, and a constant 
induced alternating current obtained, the character of which 
would be like that in the primary circuit. When an electro- 
magnet is supplied with an alternating current, the polarity 
reverses with each reversal of current so that the magnet's 
field is continually in motion, and will be cut by any conductor 
in its vicinity. The alternating-current transformer is depend- 
ent on this principle (If 357). 

Fifth Method : Moving the Iron Core. — If a piece of iron 
be so moved, relatively to the primary and secondary circuits, 
that it increases the magnetic lines of force of the primary 
circuit, an inverse current is induced in the secondary, lasting 
only while the increase takes place. When moved so as to 
produce a decrease of primary lines a direct induced current 
results. This principle is used in the inductor type of alternat- 
ing-current generator. The induction is produced by rotating iron 
poles between the stationary primary and secondary circuits. 

The character and methods of producing induced currents 
may be summarized as follows: 

Table XVI. Induction Currents 



By means of 



Magnet 
Current 



Momentary Inverse currents 
are induced in secondary 
circuit 



While approaching. 

While approaching, or 
beginning, or increas- 
ing in strength. 



Momentary Direct currents 
are induced in secondary 
circuit 



While receding. 

While receding, or end- 
ing, or decreasing in 
strength. 



Experiment 85. — With the student's induction coil (Fig. 268) all of, 
the above cases should be verified and the results noted. To ascertain 
whether the induced current is a direct or inverse one the relation between 
the galvanometer deflection and the current should be determined, as 
in Experiment 84. 



336 LESSONS IN PRACTICAL ELECTRICITY 

253. Variation of Induced E. M. F. with the Rate of Change 
of Magnetic Lines of Force. — Faraday's Law. — To produce 
induction in a closed coil located in a magnetic field it must be 
so moved that the number of fines of force threading through 
it are constantly changing. 

The induced E. M. F. is proportional to the rate of change of 
the magnetic lines threading through the coil. For example, take 
the closed coil of wire, A (Fig. 271), located in a uniform mag- 
netic field, NS, with its plane at right angles to the lines of 
force. When the coil is moved vertically downward across 
the field to position B, magnetic lines of force are cut, but no 
induction results since the number of lines of force threading 




Fig. 27L — No Induced Current in a Coil when it is Moved so that 
there is no Change of the Magnetic Lines through it. 

through the coil have not been altered. From another view- 
point the upper half of the coil cuts the lines in the same direc- 
tion as the lower half, consequently the direction of the in- 
duced E. M. F. in each half is the same, or the E. M. F.'s are 
opposed to each other, and, being of the same value, no cur- 
rent can flow. If the coil A is held either in a vertical position 
or at an angle, and then moved across the field in the direc- 
tion of the arrows to either position C or D, no induction will 
take place for the same reason. 

If the coil be now turned from its vertical position, A (Fig. 
272), by say 45° to the position B, the number of lines of force 
threading through it will be altered (decreased), and during the 
angular motion an induced current flows around the ring in 
the direction of the arrow. In this case each half of the coil 
cuts the fines of force in an opposite direction from the other, 
consequently the induced E. M. F.'s are also opposite in direc- 
tion and therefore add to each other, and set up a current 
which flows around the ring. When moved. through the next 
45°, or from B to C, the rate of change of magnetic fines through 



ELECTROMAGNETIC INDUCTION 337 

the coil continues, and is greater than when it is moved from 
A to B. This will be seen by noting the comparative number 
of lines about coil B, which pass over it instead of threading 
through it at this angle of inclination, 45°, and have, so to 
speak, been emptied out. At the position of coil C, all the 
lines of force above it have been emptied out of the coil, and the 
rate of change at this position is a maximum. The induced 
E. M. F. then varies from in position A, to its maximum 
value at position C, 90° from A. 

If the motion of the loop be continued from C to D, many 
lines of force will now be included by the coil and induction 
will occur. The direction of the current, as found by the right- 



Fig. 272. — Phases of Induction in a Closed Coil Rotated in a Magnetic 
Field — Principle of the Generator. 

hand rule, is indicated in the figure. The induced E. M. F. grad- 
ually decreases during the motion from C to D, because the 
rate of change in the number of lines of force decreases in 
the same ratio as it increased during motion from B to C. 
Motion from D to E corresponds to that from A to B, and in 
E all the lines are again flowing through the loop, causing no 
induction at this position, since there is no rate of change of 
magnetic flux. During the revolution of the coil through 
180°, from position A to E, the E. M. F. gradually increases 
from to a maximum at 90°, and gradually decreases again 
to at 180°. The same will be true of the second half of the 
revolution, 180° to 360°, except that the direction of current 
is the reverse, since moving a conductor up past lines of force 
produces a current of opposite direction from that obtained 
when it is moved down past the same lines. In one revolution 
of the coil there are thus two alternations of current, and two 
points of maximum E. M. F., at 90° and 270°. and two points 



338 



LESSONS IN PRACTICAL ELECTRICITY 




of zero E. M. F. — that is, when the current changes its direc- 
tion at 0° and 180°. When this loop is mounted on a shaft 
and rotated, we have a simple alternating-current generator, or 
alternator (11276). 

Faraday's Law is as follows: Let any conducting circuit 

BE PLACED IN A MAGNETIC FIELD; THEN, IF BY A CHANGE IN 
POSITION OR A CHANGE IN THE STRENGTH OF FIELD THE 
NUMBER OF MAGNETIC LINES OF FORCE PASSING THROUGH 
OR INTERLINKED WITH THE CIRCUIT IS ALTERED, AN E. M. F. 
WILL BE INDUCED IN THE CIRCUIT PROPORTIONAL TO THE 
RATE AT WHICH THE NUMBER OF LINES IS ALTERED. 

Fig. 273 shows how a coil of wire may have an E. M. F. 
induced in it by moving it without rotation in a non-uniform 

magnetic field. In the 
position of the coil shown 
by the solid lines, the 
number of lines of force 
through it is less than in 
the dotted position, con- 
sequently an E. M. F. is 
induced during a move- 
ment from one position to 
the other. The direction 
of current in the coil is found by the right-hand rule, and is 
such that if the ring be viewed from the side toward the N-pole 
as it is being moved away from this pole the induced current 
flows around it clockwise, producing a S-pole on this face, with 
resulting attraction for the N-pole from which it is receding 
(Lenz's law, 11251). Muscular or mechanical energy must, 
therefore, be expended in moving the ring toward or away from 
the magnet. 

254. Eddy Currents. — When a permanent magnet is sup- 
ported over a copper disk and the disk rotated, currents are 
generated in the disk, which tend to oppose the motion produc- 
ing them. If the magnet be free to move it will be dragged 
around in the same direction that the disk rotates. According 
to Lenz's Law, the current in that part of the disk moving to- 
ward the magnet pole will be in such a direction that a magnetic 
field is set up of the same polarity as the pole being approached, 



Fig. 273. — The Induced E.M.F. De- 
pends upon the Rate of Change of the 
Magnetic Lines through the Coil — 
Faraday's Law. 



ELECTROMAGNETIC INDUCTION 339 

therefore tending to repel the magnet, while the current in 
the receding part of the disk will be in such a direction as to 
produce a field of the opposite polarity, thus attracting the 
magnet. Both actions, then, tend to urge the magnet in the 
same direction and to cause its rotation. If the magnet be 
held stationary andvthe disk revolved considerably more force 
must be applied to turn it than when the magnet is not near 
it. Each part of the disk, as it comes under the influence of 
the magnet, is subjected to rapidly succeeding increases and 
decreases in the number of fines of force threading it. 

Such currents induced in masses of metal either by being 
rapidly cut by the moving field or by moving in the field are 
caUed eddy currents. The direction of the eddy currents in 
the copper disk for a particular case is shown in Fig. 274. The 
magnet is stationary and the disk rotated , 
clockwise. The currents circulate around •""'^''^ ^ 



the disk in the form of two semi-circles. 
In the left-hand one the direction is anti- 
clockwise, producing a N-face on the disk 
which repels the N-pole of the magnet, and n-^T^^^^^ ) 

M ^ M M x-u X- J • -x r^ Pivoted Copper Disc^ 

tends to stop the motion producmg it. On 

the right-hand side a S-face is produced, ^ -^^S- 274. — Eddy 
,: ,1 -_ , , . , ,. ' Currents Induced in 

attracting the N-pole, and again tending ^ Copper Disk Ro- 
to stop the motion of the disk, according tated under a Sta- 
to the Lenz's Law. When the magnet is ^^l^Z\.^ Permanent 
free to move, it will tend to move so that 
its poles will always be over the unfike poles induced in the 
disk, but as soon as the magnet moves the paths of the eddy 
currents also change. They will always be set up with the 
magnet as their diameter, and each half of the disk will be of 
opposite polarity to that of the other. The position which the 
magnet seeks is never attained and continuous rotation results 
as long as the disk is rotated. 

If pieces of wire gauze are pressed against the disk directly 
under each pole of the stationary magnet (Fig. 274) forming 
wiping contacts, or brushes, and the brushes connected to a 
galvanometer, the needle will be deflected by the eddy cur- 
rents when the disk is rotated. Faraday's disk dynamo con- 
sisted of a copper disk rotated between the two poles of a 





340 LESSONS IN PRACTICAL ELECTRICITY 

magnet (Fig. 275), the current being led off from the edge of 
the disk and returned to the center by brushes. Barlow's wheel 
(Fig. 164) when rotated by hand will give current to an ex- 
ternal circuit, illustrating the convertibility of a dynamo. 

A compass needle in a metal case will come to rest very 
quickly, because by its oscillating motion it induces eddy cur- 
rents in the case which tend to stop the 
motion of the needle. Eddy currents cir- 
culate in the metallic bobbin of the D'Ar- 
\Coppp sonval galvanometer coil when it moves in 
_. ,. ^ its magnetic field and tend to stop the 

Direction . ^ t • /^ 

ofRofafion motion accordmg to Lenz s Law. It is for 

Fig. 275. — Eddy this reason that the Weston instruments 
Currents Utilized in are SO dead-beat. The damping action 
namo^.''^'' ^''^ ^^" ^^^^ ^^^es place in the copper disk ro- 
tated between permanent magnets in the 
Thomson watt-hour meter, ^ 224. 

The eddy currents circulating in solid conductors are converted 
directly into heat and are the source of much loss of energy in 
generators, motors and transformers. To avoid them as far 
as possible, the solid conductor, such as the iron core of a 
dynamo armature or transformer, is made up of laminations, 
the plane of which is parallel to the lines of force of the field. 
The thinner the laminations the less will be the loss due to 
eddy currents. 

Experiment 86. — Strongly magnetize a bar electromagnet and strike 
one pole with a piece of fiat siieet copper and you observe a cusiiioning 
effect. You are unable to strilce tiie pole witli as great force as wiien tlie 
current is off. Eddy currents are induced in the copper, the reaction of 
the magnetic field of which tends to oppose the motion. The same is 
true if you try to lift the sheet of copper from the pole quickly. 

Experiment 87. — Suspend a copper penny by a thread between the 
poles of a horseshoe electromagnet. Twist the thread up and permit it 
to unwind. Send a current through the magnet and the motion of the 
penny will cease, due to the reaction of the eddy currents. When the 
circuit is broken the thread carrying the penny continues to untwist. 

255. Magnetic Hysteresis. — Another source of energy loss 
in the iron or steel parts of electrical machinery that are sub- 
jected to rapid changes in magnetization is called hysteresis 
(pronounced hister-ee'-sis) , See ( If 293) . 



ELECTROMAGNETIC INDUCTION 341 

Experiment 88. — The rapid magnetization and demagnetization of the 
iron core of an electromagnet, for example by an alternating current, 
produces heat as a result of the molecular friction between the particles 
of the iron. Excite an electromagnet from a source of alternating current. 
If it has a solid iron core it will get quite hot because of the eddy currents 
induced in it and because of magnetic hysteresis. The cores of alternating- 
current electromagnets -are made of bundles of wire to increase their 
resistance to the flow of eddy currents. 

256. Mutual Induction. — The induction due to two inde- 
pendent electric circuits reacting upon each other is called 
mutual induction. The previous examples of induction in a 
secondary circuit due to current flowing in the primary circuit 
illustrate mutual induction. Parallel conductors carrying 
independent alternating currents react upon each other by 
reason of the mutual inductive influence between them. Mutual 
induction in telephone circuits often gives rise to cross-talk 
unless the line is so constructed that the induction effects are 
neutralized (11260). 

257. Self-induction. — Self-induction is defined as the cut- 
ting of a wire by the lines of force of the current flowing through 
it. When a current begins to flow along a wire the magnetic 
whirls spring outward from the center of the wire and cut it. 
This cutting of the wire by its own lines of force induces in 
it a momentary inverse E. M. F., or an E. M. F. which opposes 
the applied E. M. F., and it is called a counter E. M. F. With 
a steady impressed electromotive force the induction in a 
circuit is only momentary, therefore, a brief interval of time 
must elapse before the current in the circuit reaches its normal 
value. When the current flowing through the wire is stopped, 
the magnetic field collapses, and in so doing again cuts the 
wire, but in the opposite direction. A momentary induced 
E. M. F. is set up which is now direct, or in the same direction 
as the applied E. M. F. The effects of self-induction are, 
therefore, to oppose the starting of a current by reason of the 
inverse E. M. F. which must be overcome before the current 
can reach its full value, and to momentarily retard the cessa- 
tion of the current by reason of the direct induced E. M. F. 
when the circuit is broken. Momentary currents of self- 
induction are also produced in any circuit by any change in 



342 LESSONS IN PRACTICAL ELECTRICITY 

its current strength, whereby the number of lines of force 
surrounding or interlinked with it is increased or decreased. 

The effects of self-induction are very marked in circuits 
having the form of a hehx, for in these circuits the magnetic 
field of every turn cuts many adjacent turns and the counter 
E. M. F. is increased, being proportional to the number of turns 
and the rate of change of magnetic flux through the coil. When 
the coil contains an iron core the effects of self-induction are 
vei^y much greater. 

One very noticeable effect of self-induction is the bright spark 
appearing at the point where a circuit containing wire wound 
around an iron core is broken (see Ij 262). But little effect is' 
1 1 Battery noticed on closing such a circuit on ac- 

illl \ count of the counter E." M. F., but at 



'^Switch 

Golv. 



<D 



Helix 



KMW 



X^'^-Switcti I ''break" a spark appears, due to the 

momentary induced E. M. F. which 
tends to prolong the current in the cir- 
cuit. The more rapidly the current is 
brought to zero the greater will be the 

^ induced E. M. F. The induced E. M. F. 

F i g. 276. — E X p e r i- at break is very likely much higher than 
ment Illustrating Self- the apphed E. M. F. If the terminals 
uc ion. ^^ ^j^^ point of break of a circuit contain- 

ing a coil are held, one in each hand, and then separated, the 
body will receive a shock, the intensity of which will depend 
upon the size of the coil and the amount of current used. No 
shock will be felt upon placing the hands across the battery 
in that circuit, thereby indicating that the E. M. F. of self- 
induction is much higher than the battery E. M. F. 

Experiment 89. — Connect a galvanometer in parallel with a helix of 
fine wire (Fig. 276). Close the circuit and the current will divide between 
the galvanometer and the helix; as' a result the galvanometer needle will 
be deflected, say to the right of zero. Move the needle, by hand, back 
to the zero position, and place some obstacle in the way, so as to prevent 
it turning again to the right of zero. Now release the battery key and a 
momentary current, due to the self-induction of the helix, will flow through 
the galvanometer, momentarily deflecting its needle in the opposite direc- 
tion. The induced current through the helix, at break of the circuit, is 
in the same direction as the battery current was, but flows in the opposite 
direction through the galvanometer connected to it. This is shown by 
the dotted arrow in the figure. 



ELECTROMAGNETIC INDUCTION 



343 



ElecfromagneJ- 



Experiment 90. — In Fig. 277 an incandescent lamp is connected in 
shunt with an electromagnet and through a switch to a battery of an 
E. M. F. equal to that required by the lamp. 
The resistance of the magnet should be such that 
with current flowing the lamp filament is just 
perceptibly red. At the instant of closing the 
switch the momentary iriduced E. M. F. of seK- 
induction opposes the growth of current in the 
electromagnet, causing most of the current to 
flow through the lamp, which glows brighter for 
a moment and then becomes dim as the current 
attains its steady value in the electromagnet. On 
opening the key the lamp again glows very bril- 
liantly since it is still in circuit with the electro- 




X rpu ^ r.A ■ ^\. ^\r.(kr^A Hieut lUustTating Self- 

magnet. The energy stored m the magnetic field ,-^H„pi;^^ ^ 

is thus converted into a momentary direct current 

of a high E. M. F. and illuminates the lamp. 



Fig. 277. 
3nt 
induction. 



Experi- 



The field coils of a dynamo should not be broken when 
fully excited since the E. M. F. of self-induction may become 
so high as to cause a puncture of the insulation at two or more 
points and thus complete the circuit through the iron core, 
and cause a ground. The self-induction at the break of such 
a circuit is termed the field discharge. Sometimes multi-blade 
switches are used in field circuits so that they may be opened 
simultaneously at a number of places, thus reducing the danger 
of breakdown of the insulation. 

258. Inductance. — The cause of the self-induction is due 
to the property possessed by the wire or coil called inductance, 
which is a measure of the amount of magnetic flux which may be 
associated with the electric circuit. A coil or wire possesses 
inductance whether current is passing through it or not. The 
amount of inductance offered by a coil depends on the num- 
ber of turns of wire in the coil and on the magnetic conductivity 
of the medium surrounding it. A coil of 50 turns wound around 
an iron core has a very much higher inductance than a coil of 
50 turns without an iron core. A coil of 15 turns wound on an 
iron core has less inductance than one of 60 turns wound on a 
similar core. The inductance of a coil or circuit is measured 
by the E. M. F. induced in it when the current varies at any 
given rate. The unit of inductance (the symbol for which is 
"L") is called the henry, and is the inductance of a circuit 



344 LESSONS IN PRACTICAL ELECTRICITY 

in which the induced E. M. F. is one volt when the current 
through the circuit varies at the rate of one ampere per second. 
Thus, if the current in a circuit varies at the rate of 10 amperes 
per second and induces an average of 120 volts, the inductance 
of that circuit is 12 henrys. The secondary coil of a 2-inch 
spark coil has an inductance of about 50 henrys; a 2.5-ohm 
electric bell, 0.012 henry or 12 miUihenrys; the field coils of 
a certain 3.5-kw., 110-volt, shunt-wound dynamo, 13.6 henrys. 
The inductance of an air-core solenoid of average radius 
r inches, of length 1 inches and of n turns of wire is approximately 

Inductance L = — - — 10 ~ ^ henrys . . (98),. 

Thus a coil of 1000 turns formed into a solenoid 10 inches long 
and 2 inches average radius would have an inductance of 
1000 X 1000 X 2 X 2 - (10 X 107) ^ 0.04 henry. 

With a direct current flowing in a circuit containing in- 
ductance, there is no inductive action after a stead}^ flow of 
current has been established, which usually requires only a 
fraction of a second. In this case the inductive action is 
only momentary, that is, at the instant of closing the circuit, and 
upon breaking the circuit. With an alternating current, how- 
ever, since the current is continually varying in value, the effect 
of self-induction will continue as long as the current is main- 
tained and will greatly reduce the flow of current in the circuit. 
The effect of self-induction in an alternating-current circuit can 
be illustrated by Experiments 91 and 92. 

Experiment 91. — In Fig. 278 a solenoid C, of several ohms resistance 
and wound in the ordinary manner, is connected in series with an incan- 
descent lamp L to a source of direct current (D. C.) by throwing the switch 
S down. Tlie brilhancy of the lamp is practically the same with the 
solenoid in circuit as when it is cut out by depressing key K. Neither is 
there any change in the brilliancy of "the lamp when an iron core is inserted 
in the coil. Then connect the circuit to a source of alternating current 
(A. C.) by throwing S up. With the solenoid out of circuit the lamp is illu- 
minated as brilliantly as before, but when it is inserted by opening key K 
the lamp burns dimly. The current through it has been decreased by the 
inductance of the solenoid. If an iron core is now gradually inserted 
in the coil, the current is gradually decreased, since the inductance is 
being increased, and the lamp may cease to be illuminated. The self-induc- 
tion chokes back the current, so that less current is taken from the line. 
A device for regulating the candle power of lamps in an alternating-cur- 



ELECTROMAGNETIC INDUCTION 



345 




Fig. 278. — Effect of 
Self-induction. 



a 






-Mains 

Fig. 279. — Effect of 
Self-induction. 



rent circuit is based on this principle, and is called a choke coil. The flow 

of alternating currents can thus be regulated 

much more economically than that of direct 

currents, since in the latter case regulation is 

effected by absorbing the energy in resistance. 
Experiment 92. — Thp following measure- 
ments made on a solenoid when carrying a 

direct and then an alternating current will 

further illustrate the property of inductance. 

In Fig. 279 the coil AB, without an iron core, 

is connected in series with an ammeter and to 

a source of direct-current. The pressure re- 
quired to cause a known current to flow 
through the coil is, say, 30 volts. The 
coil is then subjected to an alternating 
pressure of such a value that the current 
through it, as indicated by the ammeter, is 
the same as before, and the potential dif- 
ference across it is found to be 100 volts. 
A pressure of 100 volts alternating current 
is, therefore, required to send the same 

current through the coil as was maintained by 30 volts direct current. The 

difference in the two pressures is due to the inductance of the solenoid. 

259. Reactance and Impedance. — When an alternating cur- 
rent flows through a circuit containing inductance, the flow of 
current through the circuit is reduced, there being an apparent 
additional resistance offered to the flow of current. The cause 
of this apparent additional resistance is due to the effect of 
self-induction, and is termed inductive reactance. Reactance is 
the effect of self-induction expressed in ohms. The reactance 
in any circuit is measured in ohms, and is equal to 6.28 times 
the product of its inductance in henrys and the number of 
times the current flow is reversed per second (i.e. frequency 
of the alternating current) (1[344). The joint effect of resis- 
tance and reactance is called impedance. Ohm's Law, in its 
simplest form, is thus not applicable to calculations of circuits 
for alternating currents (1J350). 

260. Neutralizing the Effects of Self-induction. — Induc- 
tive and Non-inductive Circuits. — Self-induction in a coil may 
be neutralized by winding one-half of the coil in a right-hand 
direction and the remainder in the opposite direction. This 
is accomplished in practice by folding the length of wire to be 
used at its middle point and starting at this point, winding 



346 LESSONS IN PRACTICAL ELECTRICITY 

both halves at the same time as a single wire until the 
terminals are reached. The magnetic effects of the current 
flowing in one direction neutralize those of the same current 
flowing in the opposite direction, and the coil now offers 
practically no reactance but the same resistance to either an 
alternating or direct current. Such a circuit is said to be 
non-inductive, while an ordinarily wound coil constitutes an 
inductive circuit. No polarity would result from inserting 
an iron core in a non-inductively wound coil since the current 

> Currenf -Carrying IV/re - >. 



OZHiK " j^-"-Transpos/f/or7S — ^ b=^ 

C •< «< < D 

Fig. 280. — Transposition of Telephone Lines to Eliminate the 
Mutual Induction by Neighboring Wires. 

through one-half of the turns would tend to magnetize the core 
oppositely to that through the other half. 

An incandescent lamp is practically a non-inductive resis- 
tance, while an electromagnet is an inductive resistance. The 
coils of laboratory rheostats and Wheatstone bridges are 
wound non-inductively, so that they will have no magnetic in- 
fluence on a galvanometer, and also so that the currents in the 
bridge arms may reach their maximum values simultaneously. 

Mutual induction between parallel wires in the same circuit 
is reduced by running the wires as close together as possible. 
In alternating-current lighting and power circuits the lead 
and return wires are sometimes in the form of concentric cables 
for this reason. Mutual induction also occurs between two 
parallel circuits, as for exaraple in telephone wires running 
close to electric lighting, street railway or power lines, which 
lines carry relatively heavy currents fluctuating in value and 
setting up induced currents in the telephone circuit close to 
it, rendering the telephone circuit '' noisy." Such inductive 
disturbance may be ehminated by transposing the telephone 
wires as shown in Fig. 280. Here the " current-carrying wire " 
represents an electric lighting or power line running near and 
parallel to the telephone line wires which are shown transposed. 



ELECTROMAGNETIC INDUCTION 347 

The effect of transposing the wires is to make the average 
distance between the inducing wire and each side of the tele- 
phone circuit the same so that the total E. M. F. induced in 
wire AB will exactly equal the total E. M. F. induced in wire 
CD. Hence, the E. M. F. induced in one telephone wire will 
neutrahze that induced in the other and thus ehminate noise 
in the telephone receiver. The induction between two or more 
parallel telephone circuits may be detected by the faint sound 
of voices in the receiver, causing what is termed " cross-talk." 
The ^' twisted pair " wire generally used for telephone circuits 
is an example of transposed wires and effectively ehminates 
mutual induction in such circuits. 

QUESTIONS 

1. What is meant by electromagnetic induction? 

2. If a permanent magnet is placed inside a coil of -^dre, and then 
the terminals of the coil connected to a galvanometer, will the needle of 
the instrument be deflected? Give a reason for your answer. 

3. In Question 2, after you have connected the galvanometer to the 
coil, suppose you withdrew the magnet from the coil, in what direction 
would current flow around the coil as viewed from the end from which 
you withdrew the magnet? 

4. How long does an induced current last? 

5. How would you determine the direction of the induced E. M. F. 
in a wire that is moved past one .of the poles of a magnet? 

6. What determines the value or magnitude of an induced E. M. F.? 

7. Why is more force required to thrust a magnet inside a coil when 
the coil terminals are connected together, than when the terminals are 
not connected so as to form a closed circuit? 

8. What is the law that governs the direction of the induced E. M. F. 
in all cases of electromagnetic induction? 

9. State Faraday's Law of induced E. M. F. 

10. How may a conducting circuit be moved across a magnetic field 
so that there will be no current induced in it? Illustrate your answer. 

11. What are eddy currents and of what use are they? 

12. Explain what is meant by mutual induction, and seK-induction. 

13. What is inductance? 

14. How may the effect of self-induction be neutralized in coils of wire? 

15. How is the effect of mutual induction between parallel circuits 
neutralized? 

16. Calculate the inductance of an air-core solenoid having 2000 turns, 
a length of 20 inches and a mean radius of 1 inch. 

17. What E, M. F. is induced in the coil of the preceding problem if 
the current through it drops from 25 amperes to zero in 0.01 second? 



LESSON xxn 

PRACTICAL APPLICATIONS OF ELECTROMAGNETIC 
INDUCTION — TELEPHONY 

Practical Application of Induction — The Spark Coil — Principle of the 
Induction Coil — Action of the Condenser — Construction of In- 
duction Coils — Table XVII — Interrupters for Induction Coils — • 
Induction Coils for Automobile Ignition Systems — Vacuum Tubes — 
X-Rays — The Fluoroscopic Screen and Fluoroscope — The Tele- 
phone — Telephone Systems — Telephone Switchboards in Central 
Offices — Questions. 

261. Practical Application of Induction. — The principles 
of induction have been applied to many practical problems. 
The principle of self-induction, (1| 257) is utilized in the pro- 
duction of a spark to ignite the gas in an electric gas lighting 
system and in the ignition system of a gas engine, both 
being accomplished by the use of a spark coil (If 262). The 
principles of mutual induction are utilized in the induction 
coil (H 263), sometimes called a " Ruhmkorff coil " or '^ jump- 
spark coil"; the induction coil is of considerable importance 
in telephone circuits, in small radio telegraph sets, for X-ray 
work, and in the ignition systems used in connection with 
gasoline engines driving automobiles. The induction coil 
differs from the spark coil referred to above in that it has 
two windings, while the spark coil has but one; the induction 
coil is consequently enabled to develop higher electromotive 
forces than the spark coil for the same speed of interrupting 
the circuit, and as a result sparks may be established over 
fairly long air gaps. 

262. The Spark Coil. — The spark coil merely consists of 
many turns of low-resistance insulated copper wire wound 
upon an iron core to form a single winding, the length of the 
core and the number of turns of wire depending on the use to 
which the coil will be put. The core is not sohd, but con- 

348 



ELECTROMAGNETIC INDUCTION — TELEPHONY 349 



sists of a bundle of soft iron wires, this construction greatly 

improves the. operation by decreasing the eddy currents. The 

construction of the coil is shown in 

Fig. 281, and the external appearance 

of a coil used for gas-engine ignition 

is depicted in Fig. 282. These coils 

are used chiefly in low-tension ignition 

to intensify the spark when a battery 

is used as the source of current. 

The spark produced is due to self- 



P''^'3}i|iM 



Fig. 28L — Gas Light- 
ing Coil. 




Fig. 282. — Spark Coil for Gas- 
engine Ignition. 



induction and occurs only at 
the instant of breaking the 
circuit, the coil being connected 
in series with the battery and 
the points or contacts that are 
used to break the circuit. 
When the circuit is closed, cur- 
rent from the battery flows 
through the coil and mag- 
netizes the core ; when the cir- 
cuit is opened, the collapsing 



magnetic field develops in the same winding a counter E. M. F. 
whose value depends on the rapidity of the break. 

263. Principle of the Induction Coil. — Induction or Ruhm- 
korff coils operate upon the principle of mutual induction 
between two coils, a primary and a secondary, the E. M. F.'s 
being produced in the secondary coil by opening and closing 
the primary circuit. The induction coil is really a '' step- 
up " transformer, its function being to transfer the energy 
delivered to the primary at a low voltage to a very high voltage 
at the secondary terminals; this high voltage being capable 
of overcoming the dielectric strength of the air and causing 
sparks to pass across an air-gap. 

While a current at low pressure may thus be transformed 
into one at a very high pressure, the latter loses in current 
w^hat it gains in pressure, so that the power in watts in the 
secondary is no greater than in the primary, but always some- 
what less, owing to various losses in transformation and in 
the resistance of the circuits. 



350 



LESSONS IN PRACTICAL ELECTRICITY 



Secondary 




Condenser 



Fig. 283. — Diagram of Connec- 
tions of an Induction Coil. 



An induction coil consists of a straight laminated core, made 
up of a bundle of soft iron wires, around which ^s wound the 
cylindrical primary coil, composed of several layers of coarse 

wire, while a secondary coil com- 
posed of thousands of turns of 
fine wire is wound over the 
primary. The i primary coil is 
connected to a battery through an 
automatic interrupter or vibrator 
(Fig. 283). At the " make " and 
|"|Zr I ^^ 1 1 1 at the " break " of the primary 

L=^ I'l'll circuit an E. M. F. is induced in 

the secondary due to the changing 
magnetic flux threading through 
the secondary, and this high in- 
duced E. M. F. produces a series of sparks capable of passing 
through several inches of air from one secondary terminal to 
the other. The 
general appear- 
ance of such a 
coil is shown in 
Fig. 284, and its 
connections in 
Fig. 283. 

The interrupt- 
er or vibrator is 
a strip of spring 
brass or steel fit- 
ted at one end 
with a soft iron 
armature B, and on the opposite side near its center with a piece 
of platinum A ; the latter is in contact with a platinum-tipped 
adjustable thumb screw C, when the battery circuit is open at K. 
When the battery circuit is closed at K, the current flows from A 
to C, through the primary winding and back to the battery. 
The instant the current flows through the primary coil it strongly 
magnetizes the iron core, NS, which core attracts the armature 
B and breaks the contact of the vibrator with screw C. This 
breaks the primary circuit, the magnetism of the core ceases,. 




284. — Induction Coil. 



ELECTROMAGNETIC INDUCTION — TELEPHONY 351 

and the vibrator springs back again, " making " the circuit, 
so that the same events are repeated. The strip of spring 
metal vibrates continually as in an electric bell, and the cir- 
cuit is " made " and " broken " hundreds and perhaps a 
thousand times per ^minute. An inverse induced current in 
the secondary corresponds with each " make " of the primary, 
while a '' direct ^' current is induced on each " break " of the 
primary. Interrupted currents in the primary, therefore, 
produce alternating currents in the secondary. 

The self-induction of the primary circuit has a very impor- 
tant bearing upon the action of the coil. At " make " of the 
primary the counter E. M. F. opposes the battery current, 
and prevents the magnetic flux from rising rapidly in the core, 
while at '' break " the self -induced current in the primary tends 
to prolong or increase the primary current, preventing its 
rapid fall to zero by sparking across the contacts. A rapid 
rate of magnetization and demagnetization of the iron core means 
a great rate of change of the magnetic flux threading through the 
secondary coil, and hence a high E. M. F. A condenser, 
(^ 264) is added for the purpose of suppressing this spark 
across the primary break and of aiding the primary current 
to fall abruptly to zero. 

Experiment 93. — The primary and secondary coils, illustrated in Fig. 
268, may be mounted on a base and equipped with a contact screw and 
vibrator, so as to form an induction coil similar to that shown in Fig. 
284. Using the primary alone, the automatic action of the electric bell 
is illustrated, and when the secondary is introduced, the induced electro- 
motive forces therein may be demonstrated. When short lengths of brass 
tubing are attached to the secondary terminals of a small induction coil 
and then clasped, one in each hand, a peculiar muscular contraction is 
produced, due to the high voltage of the induced E. M. F. This is the 
physiological effect of an electric current. This should not be attempted 
with coils capable of producing sparks in air between their secondary 
terminals. 

264. Action of the Condenser. — A condenser for an in- 
duction coil consists of two sets of interlaid layers of tin-foil 
separated by sheets of paper coated with paraffin or a mixture 
of beeswax and rosin (Fig. 285). The alternate layers of tin- 
foil are connected to each other, and two common terminals 
are thus formed, as depicted in Fig. 286. There is no electrical 



352 



LESSONS IN PRACTICAL ELECTRICITY 




Tin Foil 



Paper 



Tin Foil 



Paper 



Fig. 285. — Details of 
Condenser Construction. 



connection between the condenser terminals, but if they are 
connected to a source of E. M. F. the plates become electrified 
or charged, after which they may be discharged when a proper 
path is afforded. The condenser is located in the base of 
the coil shown in Fig. 284, and its ter- 
minals connected across the primary 
break, points A and C of Fig. 283. 

The condenser action is as follows : when 
current flows through the primary at 
''make" (Fig. 283), no energy can be 
stored up in the condenser because it is 
short-circuited by the contacts. At 
" break " the E. M. F. of self-induction 
in the primary, instead of overcoming the 
resistance across the contacts, charges the 
condenser. At " break " also there is a 
complete discharge circuit for the condenser back through 
the battery and the primary coil, and takes place in the oppo- 
site direction to the previous primary current; the condenser 
thus aids in quickly demagnetizing the iron core by tending 
to set up magnetic flux in the oppo- 
site direction. If the primary circuit 
is again completed before the reverse 
condenser current disappears, as is 
practically the case,- the condenser is 
short-circuited by the contacts and 
the remaining charge is quickly dis- 
sipated. In consequence, the ' pri- 
mary current can be quickly brought to zero ; this means a rapid 
decay of magnetic flux and a high secondary E. M. F. Since 
the primary current (and thereby the magnetic flux) cannot 
rise near as rapidly as it decays because of the condenser, the 
secondary discharge becomes practically an intermittent current of 
high voltage in one direction only. In medical induction coils 
where no condenser is used the secondary charges are more 
nearly equal. 

265. Construction of Induction Coils. — Induction coils 
may be divided, according to their use, into two general classes, 
medical or therapeutic coils and jump-spark coils. In the 




Fig. 286. — Plates of a 
Condenser Assembled and 
Connected. 



ELECTROMAGNETIC INDUCTION — TELEPHONY 353 




Fig. 287. 



Electrodes 



Connections of Medical 
Coil. 



former, the secondary winding has a lower number of turns of 
wire than the secondary of an induction coil intended for 
producing sparks, so that its E. M. F. is lower, and can be 
impressed upon the human body. Some means for varying 
the intensity of the shock is provided, such as altering the 
number of turns in circuit 
in the secondary coil by a 
selector switch, Fig. 287, 
or by so constructing the 
secondary that it may be 
gradually withdrawn from 
the primary, or by varying 
the position of a brass tube 
inclosing the iron core. In 
the latter arrangement the 
tube acts as a short-cir- 
cuited secondary winding 
and has eddy currents in- 
duced in it; it therefore takes energy from the regular secondary 
winding and weakens the latter. 

The iron core is composed of a bundle of soft charcoal-iron 
wires, about No. 22 gage. For medical coils the number of 
layers in the primary is generally from 4 to 6 and the size of 
wire used No. 24, 22, or 20 B. & S. gage, according to the 
diniensions of the coil, while the secondary is usually wound 
with No. 34 or 36. 

The primary winding has considerable inductance, and this 
may be utilized by connecting the " shocking " electrodes across 
the point of '' break " of the current in the primary as shown 
in Fig. 287, where the electrodes are connected across the points 
Pi P2. The electrodes will have a potential applied to them 
only at the instant the circuit is broken by the vibrating spring 
due to the self-induction effect of the primary winding. When 
the " shocking " electrodes are connected to the terminals Si 
S2, a higher voltage is applied to them both at the make and 
break of the primary circuit, in opposite directions, due to the 
mutual induction between the primary and secondary windings. 

Jump-spark coils are usually rated according to the number 
of inches that the spark will jump between the secondary 



354 



LESSONS IN PRACTICAL ELECTRICITY 



terminals through the air. Thus a two-inch coil means that 
the E. M. F. is high enough to cause sparks to pass when 
the terminals are separated a distance of two inches. The 
inductance of the primary must be kept as low as possible and 
so it is wound with about two layers of insulated copper wire, 
usually from No. 10 to No. 16 B. & S. gage, thoroughly in- 
sulated from the core, and from the secondary. The sec- 
ondary is wound over the primary alter a layer or two of 
insulating material has been placed over the primary, the sec- 
ondary winding consisting of many turns of fine copper wire 
which may range in size from No. 30 to No. 40. 

When the coil is designed to produce a spark over 1.5 inches, 
the secondary should be wound in a number of sections sep- 
arated from each other by 
proper insulation. In Fig. 
288 the secondary is wound 
in seven sections in order to 
reduce the potential between 
the ends of each, the coils 
being separated by paper 
rings as shown. The sections 
must be so connected that 
the current will circulate 
through all of them in the 



Paper Insulators-Secondary Coil. 




Fig. 288. — Multi-coil Secondary of 
Large Induction Coil. 



same direction. A certain 12-inch induction coil has 64 sections 
\ inch wide in its secondary winding which aggregates 77,400 
turns of No. 33 B. & S. gage single silk insulated wire, the aver- 
age inside diameter being 5 inches and outside being 6f inches. 
The primary of this coil has 2 layers of No. 11 B. & S. gage 
cotton-covered wire wound to an axial length of 20| inches 
over an iron core 2f inches in diameter. A hard- rubber tube 
3f inches in outside diameter and having a wall f inch thick 
is part of the insulation between the two windings. 
" The voltage generally applied to the primary of the ordinary 
induction coil varies from about 4 to 25 volts, according to the 
size. A higher voltage causes excessive sparking and destruc- 
tion of the platinum contacts. Specially constructed inde- 
pendent vibrators are used with large coils which can be con- 
nected directly to an electric-light circuit of 110 volts or more. 



ELECTROMAGNETIC INDUCTION — TELEPHONY 355 

Such a vibrator is practically a relay, which makes and breaks 
the current in the independent primary circuit by means of 
another pair of platinum contact points. This circuit can also 
be supplied from a 110-volt circuit and the current regulated 
by a rheostat. 

The following table gives the sparking distance and approxi- 
mate corresponding sinusoidal E. M. F. between opposed sharp 
needle points under ordinary atmospheric conditions: 



Table XVII. Sparking Distances in Air 




Volts 


Distance 
(inches) 


Volts 


Distance 
(inches) 


5,000 


0.22 


60,000 


4.65 




10,000 


0.47 


70,000 


5.87 




20,000 


1.00 


80,000 


7.1 




30,000 


1.62 


100,000 


9.6 




40,000 


2-44 


130,000 


12.9 




50,000 


3.55 


150,000 


15.0 





266. Interrupters for Induction Coils. — Interrupters for 
making and breaking the primary circuit of an induction coil 
may be magnetic, electrolytic or mechani- _ ^ 

cal The ordinary interrupter placed g ^ 

on many coils represents the magnetic 
method, and though called a " vibrator " 
(^ 263), it is in fact a magnetic interrupter. 

The electrolytic or Wehnelt interrupter, 
a simple form of which is shown in Fig. 
289, consists of a glass or porcelain jar 
containing a dilute solution of sulphuric 
acid, H2SO4, in which is immersed a large 
lead electrode, Pb, and a small platinum 
electrode, Pt. The platinum is intro- 
duced into the electrolyte through a glass 
tube, the platinum being so arranged as to Electrolytic Interrupter, 
present a very small area, practically a point, to the electrolyte. 
If these two electrodes are connected in series with the primary 
of an induction coil in such a manner that the platinum is 



^ 




■rt: 

h 


F ' 


/ ■ 


=^-=^ 


^2^A 


^l 


jPb-_ 


\ — 


- I 


^ 


_ _ _ Pt, 


' 


V///////<'////////////////////////4 



Fig. 289. — Wehnelt 



356 



LESSONS IN PRACTICAL ELECTRICITY 



connected to the positive terminal of the source of supply, 
the current in the circuit will be subjected to regular and very 
rapid interruptions. The current flowing through the elec- 
trolyte from .the platinum to the lead plate sets up electro- 
chemical action liberating gases; the oxygen enveloping the 
platinum tip insulates it from the solution, thereby opening 
the primary circuit. The flow of current having been stopped, 
there is nothing to sustain the gas bubbles, which accordingly 
collapse, allowing the current again to flow through the primary, 
after which the above action is repeated indefinitely. The 
action is very rapid and the interruptions are sharp. The speed 
of the interrupter depends upon the area of the platinum 
exposed, the self-induction of the coil, and the voltage. This 
type of interrupter will not function well on continuous po- 
tentials less than 80 volts. 

A mechanical interrupter is- any device that will open and 
close two contact points by means of a purely mechanical 
contrivance, such as the contact wheel or " breaker " (some- 
times called the " timer ") that is used in connection with 
the ignition systems on automobiles (T[ 267), and the mercury 
jet interrupter. 

267. Induction Coils for Automobile Ignition Systems. — 

Induction coils used to pro- 
duce the spark in the igni- 
tion systems used on auto- 
mobiles have a primary and 
secondary winding and are 
equipped either with a vi- 
brator (or magnetic inter- 
rupter) or with a mechani- 
cal device for interrupting 
the current flowing through 
the primary from a battery 
or low- volt age magneto. 
The connections of the in- 
duction coil with a mechani- 
cal interrupter, the " spark 



Spark Plugs 




^Distributor 



Induction Coil-^ jfj^liJlp / 



Condenser- 



—II — ^ 



Battery 

III' 



Make and break 
contacts 



Ground connection', 
to metal frame of 
machine 



Fig. 290. — Connections of Auto- 
mobile Ignition Coil. 



plugs" and the distributor, as used in connection with a typical 
automobile ignition system, are shown in Fig. 290„ 



ELECTROMAGNETIC INDUCTION — TELEPHONY 357 



Latch 

.Notched 
Shaft 




Contact 
Spring 



291. — Contact- 



In Fig. 291 is shown the contact-maker, which consists of 
a notched shaft (having one notch for each cyhnder of the 
engine) rotating at one-half the engine 
speed, a lifter or trigger, which is pulled 
forward by the rotation of the shaft, a 
spring which pulls the lifter back to its 
original position, a hardened steel latch 
and a pair of contact points. The con- 
tact points are shown open, the lifter 
being puUed forward by the notched 
shaft ; when pulled forward as far as the 
shaft will carry it, the Kfter is suddenly 
pulled back by the recoil of the spring. 
In returning, it strikes against the latch, maker for Ignition Sys- 
throwing this against the contact spring, ^°^' 
thus closing the contact for a brief instant and allowing a cur- 
rent to flow for this instant through 
the primary winding of the ignition 
coil. The contact soon thereafter is 
suddenly broken when the lifter slips 
into the next notch, and at this instant 
a high voltage is set up in the sec- 
ondary. This high voltage is conveyed 
to the spark plug terminals in the order 
of - firing by the rotating distributor 
brush (Fig. 290), one terminal of the 
secondary winding of the ignition coil 
being connected to this distributor 
brush, the other secondary terminal 
being grounded, that is, connected to 
the frame of the engine. 

The distributor proper consists of a 
disk of insulating material in which are 
imbedded as many metal contact but- 
tons as there are cylinders in the en- 
gine ; these metal buttons connect with 
of the spark plug. The high voltage 
produced in the secondary causes a spark to jump the gap be- 
tween the insulated point and the body of the plug which is 




Fig. 292.— External View 
of Remy Contact-maker 
and Distributor for Auto- 
mobile Ignition S3^stem. 

the 'insulated point" 



358 



LESSONS IN PRACTICAL ELECTRICITY 




screwed into the cylinder head, thus completing the secondary 
circuit through the frame of the engine. The spark plug is 
simply a means of producing a gap in the secondary circuit and 
inside of the firing chamber; there is one spark plug in each 
cylinder of the engine. The points of the contact-maker are 
timed to break the circuit just at the instant when the spark 
is needed in each cylinder, at the same time the distributor 

brush makes contact with the metal 
button connected to the spark plug 
in this cyhnder. The contact- 
maker and distributor plate are 
mounted together to form one com- 
pact unit, the contact-maker and 
distributor brush being driven from 
the engine. Fig. 292 shows the ex- 
ternal appearance of the Remy 
ignition distributor and contact- 
, ' 'p 293. — Atwater-Kent ^laker, which are operated by a 
"Unisparker Magneto Replace- . ^ , /■ ^ r. i , i 

ment Unit. Single rotating shait geared to the 

engine. Means are provided for 
advancing and retarding the spark by shifting the contacting 
plate through a system of levers which terminate on the quad- 
rant of the steering wheel. An external view of an Atwater- 
Kent '' magneto replacement unit," for use on cars having an 
electric generator and storage battery, is shown in Fig. 293. It 
consists of the combined distributor and contact-maker on the 
right and the induction coil on the left, both being mounted 
into a compact unit that can be attached to the engine in place 
of a magneto. The Atwater-Kent contact-maker is of the 
form shown in Fig. 291. 

268. Vacuum Tubes. — Vacuum tubes, first devised by 
Geissler, are thin glass tubes of various shapes (Fig. 294) and 
provided at each end of the tube 
with a connection which extends 
a short distance into it. The 
tubes are partially exhausted 
and filled with either a gas or a 
liquid, and then sealed. On connecting the terminals to the 
secondary of an induction coil, and starting the coil in action, 




Fig. 294. — Geissler Tube. 



ELECTROMAGNETIC INDUCTION — TELEPHONY 359 



instead of an electric spark between the two electrodes, a beauti- 
ful discharge takes place which fills the entire tube with a lumi- 
nous glow. The fluorescent effect depends upon the material 
introduced into the tube. The high potential maintained across 
the tube causes the molecules of gas to become positively and 
negatively electrified, and the resulting attractions and repul- 
sions which occur produce a violent molecular bombardment, 
causing the fluorescent effect. 

269. X-Rays. — While experimenting with a Crookes vac- 
uum tube (a tube having a higher vacuum than a Geissler 
tube) excited from an induction coil, William C. Roentgen, 
in 1895, dis- 
covered that a 
sensitized pho- 
tographic plate, 
concealed from 
daylight, but 
lying near the 
vacuum tube, 
indicated expo- 
sure to light 
when devel- 
oped. Upon further investigation he found that a light was 
emitted from the vacuum tube, not perceptible to the human eye, 
but capable of penetrating many substances, as wood, thin metal, 
paper, etc. He called this light X-rays ; they are now also spoken 
of as Roentgen rays. When different substances are interposed 
between a protected sensitized plate and an excited vacuum 
tube capable of producing rays of this light, it penetrates them 
with different intensities, according to their density, so that 
the sensitized plate, upon development, shows the shadows of 
the objects interposed. A photographic print made from such 
a negative is termed a radiograph. When the hum?n hand 
is placed between the protected plate and the tube the plate 
is scarcely affected directly underneath the bones, because 
they are nearly opaque. Considerable Hght penetrates the 
flesh and affects portions of the plate directly underneath it. 
A print made from such a negative gives shadows of the bones 
and a faint outline of the flesh. Radiographs of animal bodies 




295. — X-Ray Tube. 



360 



LESSONS IN PRACTICAL ELECTRICITY 



can thus be made, and broken bones and foreign objects, 
such as bullets, needles, etc., accurately located. 

Tubes for the production of X-rays are a form of Crookes 
tube made of glass, with electrodes sealed in the tube. The 
air is exhausted from the tube so as to produce a high vacuum, 
the penetration of the X-rays emitted by the tube depending 
upon the degree of vacuum produced. One form of tube in 
general use is shown in Fig. 295; it has three electrodes sealed 
in it, the anode A, the cathode C and the anti-cathode B. 



Ammeter- 



High Voltage Circuit 




Connections of Coolidge X-Ray Tube. 



The cathode and anti-cathode are usually made of aluminum, 
while the anode has a platinum or tungsten target at the 
center of the tube and a long metal shield extending to the 
terminal. The electrodes are joined by platinum wires to 
the terminal clips in order to make the external connections, 
platinum wire being used through the glass because its expan- 
sion coefficient is the same as that of glass. The anode and 
anti-cathode are connected to the positive terminal of the 
source of supply and the cathode to the negative, the source 
of supply being a high-potential induction coil. In operation, 
negative charges (or electrons) are emitted from the cathode 
and focused, because of its concave surface, upon the plati- 
num target. The bombardment of the anode by these charges 



ELECTROMAGNETIC INDUCTION — TELEPHONY 361 



or cathode rays, as they are called, results in the emission of 
the X-rays from the anode. A chemical preparation is placed 
in the regulator tube D which will emit a gas, and consequently 
slightly lower the 
vacuum of the tube, 
when a high potential 
discharge takes place 
through it; this dis- 
charge is brought 
about by placing wire 
E near terminal C so 
that a spark will pass 
between these points 
when the tube is in 
operation. 

The Coolidge X- 
ray tube (Fig. 296) 
consists of a glass 
tube of the shape il- 
lustrated, exhausted 
until the proper vac- 
uum is produced. 
Supported in the 
tube is a cathode C, 
which is a filament of 
tungsten wire wound 
into a spiral, the fila- 
ment terminals con- 
necting to two brass 
pieces secured to the 

stem of the bulb, ^. ^^„ ^ , ^^ ^ ^^ ^■ 

. -1 , . Fig. 297. — Complete X-Ray Machine. i 

Similar to an mean- » i j 

descent lamp base. The filament is heated electrically under a 
pressure of 10 to 12 volts, from a storage battery, or, when 
alternating current is available, from the low-potential side of a 
transformer used to reduce the ordinary commercial voltages. A 
cylindrical tube of molybdenum with a flange, mounted con- 
centric with the tungsten filament, and with its inner end pro- 
jecting beyond the plane of the filament, acts to focus the 




362 



LESIONS IN PRACTICAL ELECTRICITY 



cathode rays from the filament upon the target. This target or 
anode consists of a single piece of wrought tungsten, A, attached 
to a molybdenum rod, which is supported by a split iron tube 

carried out to the right-hand 
end of the tube. 

The Universal Coohdge 
tube is operated with a high 
voltage produced by an in- 
duction coil or a high-tension 
transformer. The filament 
must always be lighted before 
the high-tension current is 
applied to the tube. The 
high potential is applied to' 
terminals 1 and 2 (Fig. 296), 
the positive being connected 
to terminal 2. If a high-po- 
tential transformer is used, 
some form of rectifier should 
be used in order that terminal 
2 will be positive at all times. 
The tube should not be oper- 
ated on voltages higher than 
that corresponding to a 10- 
inch needle-point spark gap 
in parallel with the tube. 

Fig. 297 shows a complete 
X-ray machine made by the 
Wappler Electric Company 
for hospitals and medical 
roentgenologists. The ma- 
chine is designed for 220-volt 
D. C. circuits and is capable of producing a 12-inch spark in 
air and an output of 150 milUamperes through an X-ray tube. 
The current output can be varied by changing the number of 
primary turns and by a rheostat in the primary circuit. Fig. 
298 shows the tubestand which supports a lead-glass tube shield 
(in which the X-ray tube rests) with an aluminum lead-lined 
cone at its bottom for limiting the area of the rays. 




Fig. 298. - Stand for X-Ray Tube. 



ELECTROMAGNETIC INDUCTION — TELEPHONY 363 

270. The Fluoroscopic Screen and Fluoroscope. — In order 
that X-rays may be used to examine objects such as the bones 
of the hand, foreign bodies in the system, etc., use is made of 
a fluoroscopic screen. This screen consists of a piece of paper 
or cardboard coated with certain crystals, as platinobarium 
cyanide, or tungstate of calcium, which fluoresce under the 
action of X-rays. • The light is of a pale greenish-yellow cast. 
If the hand be interposed between such a screen and the tube, 
the shadow of the bones can be plainly seen on the screen, 
the bones ' intercepting some of the X-rays, and thus causing 
the shadow. Wood readily allows the rays to pass through it, 
so that if an inch board be held between the hand and the 
screen, the shadow of the bones is still visible. 

In the fluoroscope such a fluoroscopic screen forms the 
bottom of a box, the opaque sides of which slant inward to- 
ward the top, where an opening is left for observation. The 
daylight is thus excluded and the shadows of objects inter- 
posed between the fluoroscope and the tube are plainly visible 
upon the enclosed screen. 

271. The Telephone. — The telephone is an instrument 
for the transmission of speech by means of an electric current. 
The principle underlying telephonic transmission is the pro- 
duction of a variation in current by a variation in resistance 
caused by the action of the sound waves of the voice at the 
sending station upon a diaphragm that controls the resistance; 
this sets up fluctuations in the electric current passing over 
the hne and causes a diaphragm at the receiving end 'to vibrate 
as the current fluctuates, thus reproducing, by means of the 
vibrations of the receiver diaphragm, the original sounds. 

The essential parts of the telephone subscriber's circuit 
are: the transmitter, which contains a resistance to be varied 
by sound waves impinging upon a diaphragm; the receiver, 
which reproduces the sound waves by means of a diaphragm, 
attracted by an electromagnet which is excited by the variable 
current; an induction coil for raising the pressure to increase 
the distance over which speech may be transmitted; the 
hook switch for completing the circuit of the " voice currents" 
when communication is desired; a ringer for attracting the 
attention of the party desired; and in the so-called magneto 



364 



LESSONS IN PRACTICAL ELECTRICITY 



sets also a battery and an alternating-current generator or 
magneto as sources of electrical supply. 

Transmitter. — A cross section of a telephone transmitter 
is shown in Fig. 299. The diaphragm, D, of thin iron or 
aluminum is placed opposite a hard-rubber mouthpiece, M, 
and behind the diaphragm is mounted a brass chamber con- 
taining the transmitter 
electrodes, which are 
polished carbon disks. The 
larger of these disks, E, is 
fastened within the brass 
chamber F, which is. 
screwed to the metal cup, 
G; the front carbon, Ei, 
is fastened to the center 
of the diaphragm and car- 
ries a mica washer, the 
outer, edge of the washer 
being clamped to the cup 
G by the chamber F. The 
space between the carbon 
electrodes is thus com- 
pletely, closed and is filled 
with coarse granules of carbon. The sound waves from the 
person speaking into the mouthpiece cause a vibration of the 
diaphragm and also of the electrode Ei fastened to it; this 
produces a variable pressure upon the granular carbon, thus 
altering its resistance and causing a variation in the current 
flowing through the transmitter. The transmitter parts 
are mounted in a metal case C, which is supported by an ad- 
justable clamp hinge.- The two electrodes are insulated from 
this case by the insulating ring R. 

Receiver. — The bipolar receiver in use by the Bell Com- 
pany is shown in Fig. 300. It consists of a horseshoe per- 
manent magnet with short soft iron pole pieces P and Pi. 
Each pole piece is surrounded by a coil of very fine copper 
wire. Directly in front of the poles is placed a very thin sheet- 
iron diaphragm, D, which must not touch the pole pieces at 
any time. One of the pole pieces attached to the permanent 




Fig. 299. — Telephone Transmitter. 



ELECTROMAGNETIC INDUCTION ~ TELEPHONY 365 



magnet is of north polarity and the other south polarity, and 
the diaphragm, which forms a part of the magnetic circuit, 
has a S-pole induced in it where the magnetic lines enter it 
and a N-pole where the lines leave the diaphragm. The 
diaphragm is constantly bent toward the pole pieces, due to 
their attraction for it. The coils on the pole pieces are so 
connected that the current when flowing in one direction will set 
up a magnetic force tending to strengthen 
the field of the permanent magnet and 
when flowing in the opposite direction 
will tend to weaken the field of the per- 
manent magnet. The diaphragm will be 
drawn nearer to the pole pieces when the 
direction of current in the coils is such as 
to increase the field of the magnet, and 
when this current ceases, the diaphragm 
will spring back to its normal position; 
when the current in the coils causes the 
magnet's field to be weakened the dia- 
phragm will recede from the pole pieces, 
and will be then drawn back toward them 
as this . current stops. With an alter- 
nating current flowing in the receiver 
coils, the diaphragm will oscillate to and 
fro in accordance with the current rever- 
sals. When used with a telephone transmitter, the receiver 
diaphragm will vibrate in the same manner as that of the trans- 
mitter, thus reproducing speech. 

Induction Coil. — The induction coil raises the voltage of 
the line curr.eiit in order to transmit telephone messages to con- 
siderable distances, this increase of voltage is necessary in 
order to overcome the line resistance. Another function of 
the induction coil is to change the pulsating direct current 
from the battery and transmitter into an alternating current. 
The construction of a telephone induction coil is practically 
the same as described in H 263; that is, it consists of an iron 
core, a primary and a secondary winding, but has no vibrator. 
The magnetic flux in the iron core increases and decreases 
according to the fluctuations in the current flowing through 




Fig. 300. — Bipolar 
Telephone Receiver. 



366 



LESSONS IN PRACTICAL ELECTRICITY 



the primary winding, which is in series with the transmitter 
and battery, the current fluctuations in the primary being 
caused by the vibration of the transmitter diaphragm as 
explained above. The varying magnetic flux thus produced 
in the iron core of the induction coil cuts the secondary wind- 
ing and sets up an induced voltage that reverses in direction 
as the magnetic field is increased and decreased, thus producing 
an alternating current. 

Hook Switch. — The hook switch, shown in Fig. 301, is used 

for disconnecting the local bat- 
tery, for holding the receiver cir- 
cuit open and for keeping the 
circuit intact for the signahng cur- 
rents when the instrument is idle. 
The switch is actuated by the 
weight of the receiver; with the 
receiver on the hook, the lever is 
held down against the action of 
the hook spring and causes two 
contacts to be held open and one 
to be held closed, thus opening 
the battery and receiver circuits 
and closing the signaling circuity 
as shown in Fig. 302. With the 
receiver off the hook, the lever 
will spring, up ward, allowing the 
switch springs to close the talk- 
ing and listening circuits, respectively, at the contacts A and B 
of Fig. 302, and to open the signaling circuit at contact C. 

Magneto. — The generator used in telephone sets for produc- 
ing the current for operating the ringer is a magneto which gen- 
erates an alternating current according to the principles of 
Lesson XXIII. The magnetic structure is composed of several 
horseshoe permanent magnets having cast-iron pole pieces be- 
tween which is revolved the shuttle armature. A telephone 
generator is provided with an automatic switch which either 
short-circuits or disconnects the generator from the line except 
when it is being used to signal the party at the other end of 
the line. A simplified form of short-circuiting switch is shown 




Fig. 301. — Cross-section of Desk 
Stand Showing Hook Switch. 



ELECTROMAGNETIC INDUCTION — TELEPHONY 367 



Line Terminals 
-O O— 

Ringer 



Magneto 



Transmitter 



Battery 



in Fig. 302, at the left-hand end of the magneto, and consists 
of the two springs D and E. The spring E makes contact 
with an insulated pin attached to the armature shaft, to which 
one end of the armature coil is connected ; the spring D is 
attached to the frame of the magneto, to which the other end 
of the armature coil is connected. 
When the generator is not being 
used, the springs D and E are in 
contact, forming a shunt across the 
generator, and its resistance is not 
introduced between the line termin- 
als. Current from the generator at 
the other end of the line can flow 
through the ringer of this telephone 
set, but not through the generator 
of that same telephone. When 
the magneto generator is operated 
the crank shaft is slightly moved 
toward the left and presses spring 
D away from spring E, thus re- 
moving the shunt and placing the 
generator into the circuit. 

The ringer used in telephone sig- 
nahng consists of the polarized bell fully described in \ 181, 
Lesson XIV. • 

272. Telephone Systems. — The connections in Fig. 302 
are those of a '' local battery system " of the class known as 
the '' series telephone set," so called because the generator 
and ringer are placed in series with each other. Another type 
of instrument more frequently used in local battery systems 
is that of the " bridging telephone set " in which the generator 
and ringer are separately bridged or connected in parallel 
across the hne (Fig. 303). In the bridging set the generator is 
provided with an automatic switch that opens the generator 
circuit when it is not in use. The switch has three springs 
instead of two, as in the series telephone, and the armature coil 
connects with the frame of the generator and with spring E. 
The connections are so arranged that when the generator is 
in use the ringer will be disconnected from the line, and when 




^^Hool< Switch 
'Receiver 

Fig. 302. — Connections of 
a Series Telephone Set. 



368 



LESSONS IN PRACTICAL ELECTRICITY 



Line Terminals 
-O O 



not in use the generator will be open circuited and the ringer 
will be connected across the line terminals. In a bridging tele- 
phone there is no lower contact for the hook switch, as shown 
in the connection of the series telephone; the only path for 
the current when the receiver is on the hook is through the 
ringer. 

In addition to the local battery system of operating tele- 
phones, there is a system known as the " common battery '' 

or "■ central energy " system 
wherein current for the talk- 
ing and signaUng circuits is 
supplied from a central or com- 
mon source instead of from 
batteries and magnetos located 
at each subscriber's telephone 
set. The common source of 
supply for the talking circuit 
is generally a storage battery 
located at the central office. 
In a common battery system 
the subscriber's telephone 
equipment is somewhat dif- 
ferent from that of a local 
battery system; for example: 
the transmitter is of higher re- 




Fig. 303. — Connections of 
Bridging Telephone. 



sistance, due to the fact that the voltage in a common bat- 
tery system is higher than in the local battery system; the 
induction coil has different windings because it is used in a 
different way, not primarily to raise the voltage, since the volt- 
age of a common battery system is generally high enough to 
effectively transmit speech over a considerable distance. The 
additional apparatus used is a condenser (Ij 264). 

The circuit of a subscriber's set in a common battery sys- 
tem is somewhat more complicated than those of the local 
battery systems ; Fig. 304 shows the connections of a common 
battery telephone set which is widely used in this country. 
The equipment consists of transmitter, receiver, ringer, in- 
duction coil, hook switch and condenser; direct current is 
supplied to operate the transmitter, while alternating current 



ELECTROMAGNETIC INDUCTION — TELEPHONY 369 



Line Terminals 
O 



Condenser.^ 
Ringer \ 

KX>i 




is generally used to operate the ringer. The function of the 
condenser is twofold: it prevents the direct current 'from 
flowing through the ringer, and improves the action of the 
induction coil, thus increasing the sensitiveness of the set. 
As an alternating current only can pass through a condenser, 
it is connected in that part of the telephone circuit through 
which the alternating current is to flow. In the different tele- 
phone connections used in practice, the points of connection 
for the condenser will differ, the condenser performing either 
or both of the above mentioned 
functions according to the system 
of connections used. 

From the diagram of connec- 
tions (Fig. 304) it can be seen that 
with the receiver on the hook no 
direct current can flow, but an 
alternating current may flow over 
the line to operate the ringer, 
since that circuit is completed 
through the condenser. With the 
receiver off the hook, the receiver 
is connected in series with the con- 
denser and both windings of the 
induction coil across the line terminals and will respond to 
the pulsating currents set up by the distant transmitter. The 
direct current from the line flows through the primary of the 
induction coil and the transmitter, and the line current while 
spealdng will fluctuate according to the vibrations of the trans- 
mitter diaphragm. 

273. Telephone Switchboards in Central Offices. — The 
lines from the subscriber's telephone sets (H^ 271 and 272) run 
to a central office and connect to a switchboard for rapidly 
interconnecting lines for conversation. A telephone switch- 
board system is designed to perform certain functions, such 
as: every subscriber may signal the switchboard operator and 
give her the required subscriber's number; any subscriber's 
line may be connected to any other line entering that office; any 
subscriber in the district served by that switchboard may be 
signaled from the switchboard; every subscriber after conver- 



Fig. 304. — Connections of 
Telephone Set iij a Common 
Battery System. 



370 LESSONS IN PRACTICAL ELECTRICITY 

sation has terminated can secure disconnection; and any two 
central offices may be connected together through their switch- 
boards so that a subscriber desiring another subscriber located 
in an entirely different district may be connected with him 
through the switchboards located in their respective district 
offices. 

The subscribers' lines are brought into the central office 
through protectors and hghtning arresters and, in manually 
operated switchboards, terminate in signals and in switch 
sockets. These switches are called jacks and consists of a 
guiding thimble behind which are arranged a number of con- 
tact springs of sheet metal. The switchboard is provided 
with flexible connecting conductors having plug terminals that 
fit properly with the contacts of the jacks. The flexible con- 
ductors are usually made in two lengths, coupled together 
to form a pair of connecting cords, and associated with each 
such pair is a switch or listening key by means of which the 
operator may connect her telephone set to them at will, and 
also a switch or ringing key for applying ringing current to the 
conducting strands of the cords. 

In the modern switchboard, the attention of the switch- 
board operator is secured by a lamp signal that is illuminated 
as soon as the subscriber lifts his receiver from the hook. 
The operator then inserts the answering plug into the jack 
of the calling subscriber's line, which act extinguishes the 
lamp; the operator then closes the listening key and thereby 
connects her telephone with the subscriber. On ascertaining 
the number of the subscriber desired, she takes the second 
cord of the pair, inserts its plug in the jack of the desired line 
and depresses the ringing key to call the subscriber. On 
inserting this plug a lamp in the cord circuit, called a super- 
visory signal, is illuminated. When the called subscriber 
answers by taking his receiver from the hook, the supervisory 
signal lamp is extinguished, and the two subscribers are in 
communication. The two subscribers can now converse, 
current being supplied from the common battery located at 
the central office. When either subscriber returns his receiver 
to the hook, he breaks his circuit, and illuminates the cor- 
responding supervisory lamp, indicating to the operator that 



ELECTROMAGNETIC INDUCTION — TELEPHONY 371 

the conversation is over. These lamps indicate at all times 
to the operator the condition of the circuits, and hence are 
called '^ supervisory lamps." There are many different tele- 
phone systems and connections in use, some of which require 
additional apparatus that cannot be treated in the space 
allotted for this subject, and the student interested in tele- 
phone work should procure some standard text treating that 
subject. 

QUESTIONS 

1. Wha,t is the difference between the current flowing from a battery 
and that from the secondary of an induction coil? 

2. An interrupted current in the primary of an induction coil pro- 
duces an alternating current in the secondary circuit. Explain fully 
how one secondary terminal can then be called a cathode and the other an 
anode. 

3. Make a complete sketch of an induction coil with condenser, 
and indicate the directions of current in the primary and secondary circuits 
at " make " and at " break." 

4. What is the advantage of using a condenser with an induction 
coil? 

5. What is the objection to using a solid iron core in constructing 
an induction coil? 

6. Make a sketch of the Wehnelt interrupter connected to an induction 
coil. Indicate the direction of currents. 

7. Describe and explain the operation of an automobile ignition 
system. 

8. Describe the Coolidge X-ray tube. 

9. What is a fluorescent screen and how is it used in X-ray examina- 
tions? 

10. Explain the principle of action of a telephone transmitter. 

11. Explain the operation of a telephone receiver. 

12. State how two telephone subscribers whose lines terminate in the 
same office are brought into communication. 



LESSON XXIII 

PRINCIPLES OF DYNAMO-ELECTRIC MACHINES 

Dynamos — Classification of Generators — A Simple Generator — Alter- 
nating-Current Generator — Graphic Representation of an Alternating 
Current — Magneto Alternator — Simple Direct-Current Generator 
— Graphic Representation of a Direct Current — Multi-Coil Arma- 
tures — Principle of the Motor — Direction of Rotation of Motors — 
Questions. 

274. Dynamos. — The term dynamo is applied to machines 
which convert either mechanical energy into electrical energy 
or electrical energy into mechanical energy by utilizing the 
principle of electromagnetic induction. A dynamo is called 
a generator when mechanical energy supplied in the form of 
rotation is converted into electrical energy. When the energy 
conversion takes place in the reverse order the dynamo is 
called a motor. Thus a dynamo is a reversible machine capable 
of operation as a generator or motor as desired. 

A generator does not create electricity, but generates or 
produces an induced electromotive force, which causes a cur- 
rent to flow through a properly insulated system of electrical 
conductors external to it. The amount of electricity obtain- 
able from such a generator is dependent upon the mechanical 
energy supplied. In the circuit external to a generator the 
E. M. F. causes the electricity to flow from a higher or positive 
potential to a lower or negative potential, just as water flows 
from a higher to a lower level. In the internal circuit of a 
generator the E. M. F. causes the current to flow from a lower 
potential to a higher potential, just as water is pumped or 
forced from a lower to a higher level. The action of a gen- 
erator is based upon the principles of electromagnetic induction, 
discovered by Faraday, and fully considered in Lesson XXL 

The dynamo consists essentially of two parts: a magnetic 
field, produced by electromagnets, and a number of loops or 
coils of wire wound upon an iron core, forming the armature. 
These parts are so arranged that the number of the magnetic 

372 



DYNAMO-ELECTRIC MACHINES 



373 



lines of force of the field threading through the armature coils 
will be constantly varied, thereby producing a steady E. M. F. 
in the generator or a constant torque in the motor. 

The general appearance of a direct-current dynamo is seen 
from Fig. 305, which shows a Type K Allis-Chalmers ma- 
chine. A disassembled view of this dynamo appears in Fig. 
306, wherein the principal parts are more clearly seen. 




Fig. 305. — Multipolar Motor or Generator. 



275. Classification of Generators. — According to their 
mechanical arrangement, generators may be divided into 
three classes: 

1. A stationary field magnet and a revolving armature, 

2. A stationary armature and a revolving field magnet, 

3. A stationary armature and a stationary field magnet, be- 
tween which is revolved a toothed iron core. 

In the first class provision is made for conducting the current 
from the armature either by collector rings (^ 277) or by a 
commutator (H 280). In the second class provision is made 
for conducting the current to the revolving field by collector 
rings, while in the third class there are no moving wires nor 
contacts. 



374 LESSONS IN PRACTICAL ELECTRICITY 

Generators may be further classified according to their 
design and mechanical construction into 

1. Direct-current generators, 

2. Alternating-current generators, or alternators. 

In direct-current dynamos the field -magnets are usually sta- 
tionary while the armature revolves (Figs. 305 and 306). In 
alternators, the armature is usually stationary, while the field 
magnets revolve (Fig. 307) ; while in some types both are sta- 
tionary while an iron core is revolved. All generators are 




Fig. 306. — Dismantled View of Dynamo. 

fundamentally alternators — that is, machines in which al- 
ternating currents are generated. When provided with a 
suitable commutator, the current from such a machine is 
made unidirectional in the external circuit, but still alternates 
in direction in the armature coils. 

A dynamo having only one N-pole and one S-pole in its 
field structure is called a bipolar dynamo. Those having 
more than two poles, such as 4, 6, 8, etc., are called multipolar 
dynamos. Modern motors and generators with stationary 
fields have their field frames constructed in ring form, as 
shown in Fig. 306, whether bipolar or multipolar. Some 
experimental bipolar machines are constructed as illustrated 
in Figs. 309 and 312. Bipolar dynamos are seldom used at 
the present time except in very small machines and in some 
large generators that are driven at high speed by turbines. 



DYNAMO-ELECTRIC MACHINES 



375 



The use of more than two poles brings with it the advantage 
of slow speed in the generation of commercial voltages. Slow 
speed is an advantage in any apparatus with moving parts, 
because there is less liability of derangement, less wear, and 
hence less need of renewal of such parts. If a two-pole gen- 
erator is required to run at 1000 revolutions per minute to 
generate an E. M. F. of 125 volts, then under otherwise equal 




Fig. 307. — Waterwheel-dri\-en Alternator with 

Revolving Field. 

Field coils are of copper ribbon wound edgewise. 

conditions a four-pole dynamo of equal voltage need run at 
only 500 revolutions; one of eight poles, at only 250 revolu- 
tions per minute. In subsequent discussions of generator action 
bipolar fields will be assumed in many cases because of greater 
simplicity. 

The field magnet cores are cylindrical or rectangular in 
form and usually constructed of cast " mild " steel (soft steel) 
containing a very small percentage of carbon, the magnetic 
quality of which is nearly equal to that of wrought iron. This 



376 



LESSONS IN PRACTICAL ELECTRICITY 



Rofcrfion 



is a much cheaper construction than where they are forged 
from wrought iron. These cores are cast- welded into the plain 
cast iron or cast steel field ring, which, in the larger sizes, is 
generally divided into two parts, for convenience in handling. 
The pole faces or shoes are generally constructed of laminated 
sheet steel, and in some machines the entire field cores are so 
made. 

276. A Simple Generator. — Consider the single closed 
loop of wire, ABCD of Fig. 308, which is mounted on a shaft 
and may be rotated by hand around its horizontal axis in the 
uniform bipolar magnetic field, NS, in the direction of the 

arrow. The direction and 
variation in magnitude of the 
induced E. M. F. is the same 
as that given under Fara- 
day's Law for the different 
positions of a loop during a 
complete revolution in Fig. 
272 and H 253.i At the posi- 
tion ABCD (Fig. 308), there 
is no E. M. F. induced in the 
loop, since all the lines of 
force of the field thread 
through it. During the first 
quarter of a revolution, the 
fines of force threading through the loop are gradually 
diminished at an increasing rate, and the E. M. F., depending 
on the rate of change of the lines of force through it, increases 
in magnitude with its direction from b to a in the right-hand 
side of the loop, and from c to d in the left-hand side. After 
it has revolved one-quarter of a revolution to the position in- 
dicated by a b c d, the plane of the loop is parallel to the lines 
of force; so that none thread through it; the rate of change is 
now a maximum, as is also the E. M. F. 

During the second quarter of the revolution the lines of 
force thread through the opposite side, which is equivalent to 
a further diminution of the lines of force through it, the rate 

^ The student is advised to read again ^ 253, which fully explains the 
fundamental principle of the generator. 




Fig. 308. — Direction and Magni- 
tude of the Induced E.M.F. in a 
Generator. 



DYNAMO-ELECTRIC MACHINES 



377 



f - *ll 


©' 


t f '-^^^ 


' fej»r^i 




iii^iiwB^OTn' ' 


ilUlK 


K^' 


^^E 





of change and the E. M. F. decreasing until at half revolution 
the E. M. F. is zero. The direction of the E. M. F. is the same 
throughout this half revolution, ■ and the current flows around 
the loop from a 
to c, to d, to b, 
to a, changing in 
strength with 
every variation 
of the generated 
E. M. F. Dur- 
ing the next half 
revolution the 
same variations 
in E. M. F. occur 
but the induced 
E.M.F. isinthe 
opposite direc- 
tion. The cur- 
rent is therefore 
reversed twice in 
every revolution, 
or an alternating 
current flows around the loop. Fig. 309 shows an Evans experi- 
mental machine for illustrating the generation of E. M. F.'s 
by coils of wire revolving in a magnetic field. The parts illus- 
trated belong to an electrodynamic equipment supplied by the 
Central Scientific Company. 

277. Alternating-Current Generator. — To utilize the cur- 
rent flowing in the foregoing closed loop when it is rotated in 
the bipolar magnetic field, some mechanical device must be 
used to lead or collect the current from the rotating loop so 
that it will flow through a circuit external to it. Two col- 
lector rings are used for this purpose and consist of metal 
rings mounted on wooden or hard-rubber hubs (Fig. 310), these 
being mounted on the shaft with the loop. The rings are 
insulated from each other and from the shaft. The terminals of 
the loop are connected, one to each ring, and stationary strips 
of copper, P and M, termed brushes, rest upon the rings and 
are connected to the external circuit. When the loop is re- 



Fig. 309. — Generation of an E.M.F. by the 
Rotation of Coils in a Biploar Magnetic Field. 

The field magnets are excited from a source of current and 
the terminals of the coil may be connected by brushes and 
lead wires to a voltmeter. 



378 



LESSONS IN PRACTICAL ELECTRICITY 



volved a sliding or wiping contact is established and the cur- 
rent is conducted to the 
external circuit. 

During one half of the 
revolution of the loop, 
ABCD of Fig. 310, the 
direction of current in AB 
is from B toward A, and 
from brush M, which is 
therefore positive, to the ex- 
ternal circuit, composed of 
incandescent lamps in 
parallel. From the lamp 
terminals the current flows 
back to brush P, the nega- 
tive brush, and around the 
loop from C to D, to B, 
etc. Now consider the 
second half revolution de- 








p ) 




f 


I 


1 


K>i 








o- 


i^ 






^^ 


iar 


np 



Fig. 310. — Simple Alternating- 
current Generator. 

At the instant depicted in the revolution 
brush M is positive. 



picted in Fig. 311. The di- 
rection of current in the 
wires AB and CD is reversed 
(right-hand rule) and current 
flows from D to C, through 
brush P, now positive, then 
through the lamps in the op- 
posite direction to that in 
Fig. 310, and through brush 
M, now negative, to AB, to D, 
etc. In every revolution of 
the coil in a bipolar field the 
polarity of the brushes 
changes twice, or there are 
two alternations of current per 
revolution in the external cir- 
cuit. The number of alter- 
nations per minute in any 
alternator equals the speed in 
revolutions per minute multi- 




Fig. 311. — Simple Alternating- 
current Generator. 

Direction of current in coil at one- 
half revolution from the position in 
Fig. 310; brush M is now negative. 



DYNAMO-ELECTRIC MACHINES 



379 



plied hy the number of poles. The number of times that one of 
the brushes becomes positive in one second is expressed as the 
frequency; thus a frequency of 60 means that during each 
second one brush is positive sixty times and also negative sixty 
times — in other words the frequency of the current is 60. 



Student's Experimental Dynamo. — A simple apparatus for study- 
ing the principles of induction and current collection in a dynamo is 
illustrated in Fig. 312, and consists of a horseshoe electromagnet fitted 
with cast-iron pole pieces and mounted on a wooden base. A rectangular 
coil of No. 26 copper wire, having 5 ohms resistance, is mounted on a 
shaft, suitably supported by a brass framework extending from the pole 
pieces. The framework also carries two insulated brush holders. At one 
end of the shaft the coil terminals are connected to a pair of collector 
rings mounted upon it, while the same terminals are also connected to a 
two-part commutator at the other end of the shaft. By reversing the 
position of the coil between the pole pieces the brushes will rest either upon 
the rings or upon the commutator. The electromagnets have a resistance 
of 1.3 ohms each and are to 
be excited from a source of 
direct current. The brushes 
may be connected to a de- 
tector galvanometer, and 
when the shaft is rotated by 
hand either the alternating or 
direct current may be studied. 
When connected as a shunt 
motor the rectangular coil 
will attain a speed of sev- 
eral hundred revolutions 
per minute with an applied 
E. M. F. of 4 volts. 

Experiment 94. — Sepa- 
rately excite the magnets 
(connected in series) of the 
student's experimental dy- 
namo, Fig. 312, so that one 
pole piece will be N and the 
other S, and adjust the 
brushes so that they will bear 
Ughtly upon the collector rings. 
vanometer, Fig. 172. 

(a) Revolve the shaft slowly and note the alternating deflection of 
the galvanometer needle. 

(b) Increase the speed and note that the needle remains at zero with 
a perceptible vibration. 




Fig. 312. ~ Student's Experimental 
Dynamo. 

Connect the brushes to the detector gal- 



380 



LESSONS IN PRACTICAL ELECTRICITY 



(c) Turn the coil to the vertical position, break the field circuit and 
note the galvanometer deflection; close the field circuit and again note 
the deflection. Why are the deflections opposite? 

(d) Reverse the polarity of the fields and repeat (c), noting results. 

(e) Turn the coil so that it is horizontal; then make and break the cir- 
cuit. The galvanometer needle is not appreciably deflected. Why is this 
so, in view of the fact that this is the position of maximum induced E. M, F. 
of a loop rotated in a bipolar field? Why is it different in this case? 

278. Graphic Representation of an Alternating Current. — 

The changes in direction and magnitude of an alternating 
current are frequently represented diagrammatically. For 
example, suppose a current of 5 amperes to flow for one second 
in one direction, and then be automatically reversed and flow 
for one second in the opposite direction, and reversed again, 

this cycle of events 
continuing at 
regular intervals 
while the current 
flows. The action 
is represented in 
Fig. 313, where 
the horizontal line, 
PK, is divided in- 
to equal distances, 
PC, OF, FK, etc., each representing one second of time. The 
vertical line, AM, at right angles to PK is divided into distances 
representing units of current, the current is said to flow in a 
positive direction when indicated above PK, and negative 
when below PK. When the switch is closed the current is 
seen to rise to its full strength of 5 amperes, or from P to A, 
and 5 amperes are maintained constant in a positive direction 
for one second, A to B. When point B is reached at the end 
of the first second the current falls abruptly to zero, B to C, 
and rises to 5 amperes in a negative direction, and is main- 
tained for an equal interval of time, D to E, when it again 
falls to zero at F, and repeats the same cycle of events in 
equal intervals of time. The Hne PABCDEFGHK is called 
the wave form of an alternating current. 

In Fig. 313 the current is depicted as being of constant 



5 


A 


B 6 




H 


4 - 

si: 










£ ' - 

4 - 


P C 

<r-l Second-^ 


F 
<-l Second--^ 


K 




5 - 


M D 




E 





Fig. 313. 



— Graphical Representation of an 
Alternating Current. 

Wave shape is rectangular. 



DYNAMO-ELECTRIC MACHINES 



381 




strength during each second, while it was shown in T[lf 253 
and 276 that during rotation of the loop the current and 
E. M. F. varied. This variation in magnitude is represented 
in Fig. 314, which is constructed similar to Fig. 313, but the 
current gradually rises 
to its maximum value 
of 5 amperes, P to A, 
and as gradually di- 
minishes again to zero, 
A to B, during the first 
second, which may 
also represent one half 
revolution of the loop. 
Corresponding with 
the second half revolu- 
tion, the current gradually rises from B, reaching its maximum 
negative value at C (three-quarter revolution), and falls again 

to zero at D, and so on. 
In an alternating-cur- 
rent generator the alter- 
nating current wave is 
not so abrupt as that 
depicted in Fig. 314, 
but more truly repre- 
sented by the undu- 
latory curve. Fig. 315, 
which represents the 



■/Second- 



Fig. 314. — Graphical Representation of an 
Alternating Current. 

Wave shape is triangular. 




Fig. 315. — Graphical Representation of 
an Alternating Current. 

Wave shape is sinusoidal. 



same general variations as before. Thus at the end of one half 
second the current reaches its maximum value, 5 amperes, 
represented to scale by the line AG, while the value of the 
current at one quarter second is equal to the line KL, or about 
3.5 amperes. 

279. Magneto Alternator. — The E. M. F. produced by a 
generator depends upon: 

(a) The number of lines of force cut by the armature wires, 

(b) The number and length of the cutting wires, 

(c) The speed at which the armature revolves. 

The E. M. F. of the single-loop armature of Fig. 311 will 



382 



LESSONS IN PRACTICAL ELECTRICITY 




Fig. 316. — Siemens Shuttle Armature. 



therefore be increased by winding it upon an iron core called 
the armature core, as in Fig. 316, which greatly increases the 

number of hnes of 
force between the 
poles N and S, 
and also by wind- 
ing a great many 
turns in the same 
direction around 
this core. Fig. 
316 illustrates a 
Siemens shuttle 
armature, which is 
revolved between the poles of the permanent magnets NS ; it is. 
called a magneto generator, because the field is produced by per- 
manent magnets. Only one 



turn is illustrated, but the 
shuttle is filled with wire, 
as in the cross-sectional 
view. This construction is 
only employed in small ma- 
chines, such as those used 
with magneto telephone sys- 
tems (Fig. 317), for gas en- 
gine ignition systems, and 
for testing insulation of 
lines. For generating large 
currents, generators are em- 
ployed in which strong fields are produced by electromagnets 
and in which the armature core is laminated to prevent exces- 
sive loss of energy by eddy currents. 

280. Simple Direct-Current Generator. — When it is de- 
sired to have the current from a generator flow always in one 
direction in the external circuit, like a battery current, for 
such purposes as charging accumulators, electroplating, etc., 
a commutator must be substituted for the collector rings in the 
simple alternator of Fig. 311. The function of a commutator 
is to reverse or commute the alternating current of a generator 
at the proper instant in each revolution before it flows through 




Fig. 317. — Magneto Generator for 
Telephone Ringing. 



DYNAMO-ELECTRIC MACHINES 



383 



the external circuit. It is prac- 
tically a split ring, mounted 
upon a hub insulated from the 
shaft, with the parts of the 
ring also insulated from each 
other. Brushes rest upon the 
split ring at diametrically op- 
posite points. The scheme 
of a simple bipolar direct- 
current dynamo is illustrated 
in Figs. 318 and 319, from 
which the act of commutation 
can be studied. In Fig. 318 
the wire AB is rotated down 
past the S-pole. The direc- 
tion of current is from B to A, 
by the right-hand rule, and to 
the external circuit by brush 
M, which is positive; then 





Lamps 



Fig. 319. — Simple Direct-current 
Generator. 

Direction of current in the coil at one-half 
revolution from the position in Fig. 318; brush 
M is positive as before. 



Lamps 



Fig. 318. — Simple Direct-current 
Generator. 

At the instant depicted in the revolution 
brush M is positive. 



from the lamps to the 
negative brush P and 
around the loop, CDBA. 
When the loop is rotated 
one half revolution (Fig. 
319), AB will move up 
past the N-pole and the 
direction of current in it 
will be reversed. Its ter- 
minal, however, is not 
now in contact with hrush 
M, as before, hut connected 
to brush P. Current 
flows to the external cir- 
cuit from the brush M, 
which is still positive, 
though the current in the 
armature has been re- 
versed, as in an alterna- 
tor. Brush M is conse- 



384 



LESSONS IN PRACTICAL ELECTRICITY 




quently always positive and brush P always negative, or the 

current in the external circuit is a direct current flowing in one 

direction only. 

The act of commutation occurs at the instant when the 

wire, moving down past the S-pole, commences to move up 

past the N-pole, each ter- 
minal of the coil being 
connected with one brush 
for one half revolution 
and with the other brush 
for the other half of the 
revolution. With a two- 
part commutator, the 
current in the external 
circuit is interrupted 
twice in each revolution. 
A single coil armature of 
Fig. 320. — The Induced E.M.F. of each several turns is shown in 

Turn is in Series with that of every other pig. 320, wherein it is seen 

that the direction of the 
current is the same for all the wires on the same side of the coil. 
In what direction is the coil supposed to be revolving in this 
figure? 

Experiment 95. — Make the same connections for the student's ex- 
perimental dynamo as given in Experiment 94. Adjust the brushes so 
that they bear lightly upon diametrically opposite points of the two-part 
commutator. 

(a) Upon revolving the shaft slowly the needle is now deflected to 
one side of the zero mark. 

(b) Reverse the direction of rotation, and the direction of deflection 
(or polarity of the brushes) is also reversed. 

(c) Increase the speed and the deflection increases. Why? 

(d) Increase the field strength by grouping the magnet coils in parallel, 
leaving the poles N and S as before; the deflection will be found greater 
than before for the same speed of rotation. Why? 

Experiment 96. — (a) Repeat Experiment 84, page 330, to determine 
the direction that the galvanometer needle deflects for a given direction of 
current. 

(b) Test with a compass the field poles of the student's experimental 
dynamo of Fig. 312 and mark the polarity of the pole pieces. 

(c) Determine, with the aid of the galvanometer, the positive brush 
for a particular direction of rotation. 



DYNAMO-ELECTRIC MACHINES 



385 



(d) Apply the right-hand rule, H 249, and note whether the polarity de- 
termined by this method agrees with that already determined. 

(e) Reverse the polarity of the fields and again prove this rule. 

281. Graphic Representation of a Direct Current. — The 

same method is appHcable for illustrating the direction and 
magnitude of a direct 
current as given in ^ 278 
for an alternating cur- 
rent. Since there is no 
reversal of current in the 
external circuit, the curve 
will lie above the time 
line (Fig. 321), and repre- 




Fig. 321. — Graphic Representation of 
a Direct-current from a Single Coil. 



<u 6 
0- 






6 X C 
/ \ 



V> \/>V.H V^dV^j 



-I Revolufion- 



-J 



sents the magnitude of E. M. F. or current at each instant 
during the rotation of the loop in the bipolar field. The curve 
indicates a pulsating current of 5 amperes maximum value flow- 
ing always in one direction. 

282. Multi-Coil Armatures. — With an armature com- 
posed of a single coil of wire the current in the external circuit 
is very pulsating as the coil passes through the various phases 

of induction represented by the 
curve in Fig. 321. In Fig. 308, 
consider two coils to be placed 
at right angles to each other; 
then, at the instant shown, the 
current in the vertical coil will 
be zero, while that in the hori- 
zontal coil will be a maximum. 
As rotation is continued the 
current in the one coil, ABCD, increases as that in the other, 
abed, decreases until, at quarter revolution, current in coil A is 
maximum and in coil a, zero, and so on. There will thus al- 
ways be current flowing in one of the two coils, so that if they 
are properly joined to an external circuit the current will be less 
pulsating than when a single coil is used. This is depicted in 
the current curves of Fig. 322, where the curve ABODE repre- 
sents the current wave from one coil and curve FGHIJ shows 
that from the other coil, and where the heavy line AKGLCMINE 
represents the pulsating character of the current produced by 



Fig. 322. — Representation of a 
Direct-current from a Multi-coil 
Armature. 



386 LESSONS IN PRACTICAL ELECTRICITY 

the two coils acting together in the same circuit. The current 
is thus never zero in the line as in the curve of Fig. 321, but 
varies from a minimum value of 5 amperes to a maximum of 
about 7 amperes. The armatures of dynamos are wound with 
many coils of wire, so that the current may be continuous in 
the external circuit. These coils are angularly disposed on the 
iron core of the armature. 

283. — Principle of the Motor. — The principles involved 
in the rotation of the armature conductors, when carrying a 
direct current and located in a magnetic field, were fully dis- 
cussed under the subject of Electrodynamics, Lesson XV. 
It was also shown in HH 214 and 224 how a single loop, placed 
in a magnetic field, could be made to rotate, by commutating 
the current through it at the proper instant in its revolution, 
and how the turning effort was increased by increasing the 
number of loops or coils and arranging them at different 
angles with reference to the field. When the loops are dis- 
tributed around an iron core, and then placed in a powerful 
magnetic field and a current passed through them, each loop 
tends to move to the position in which it encloses the greatest 
number of the fines of the field. The direction in which each 
loop will move will be such that its lines of force will be in the 
same direction as the lines of force of the field; the force with 
which it will move, or the turning effort or torque (Tf 315) will 
depend upon the strength of current flowing through it (that 
is, the strength of current driving the motor), the size of the 
loop, and the density of the lines of force through it. When 
the loop arrives at the position where it accommodates the 
greatest number of the fines of force through it in the same 
direction as its own fines, the force, or turning effort, stops. 
If moved past this position the electrodynamic force is reversed 
and now tends to turn the coil back to the position of maxi- 
mum lines of force through it. To obtain continuous rotation, 
the current through each loop must be reversed at the instant 
that the turning effort ceases. These reversals are automat- 
ically performed by the commutator, when the brushes are 
correctly set and adjusted. 

In a generator the direction of current in the armature is 
such as to oppose the motion producing it, Lenz's Law; the 



DYNAMO-ELECTRIC MACHINES 



387 



reaction increases as the current from it increases, thereby 
requiring additional power to drive it as the load increases. 
The reaction of the current in the armature of a generator is 
thus opposed to the direction of rotation of the armature. 

In a motor, the reaction of the magnetic field of the arma- 
ture conductors upon the magnetic field surrounding them is 
such as to move the armature wires across the field in the 
same direction as the armature rotates, and it is this force 
which is used to perform mechanical work at the motor pulley. 
The greater the load applied to the pulley of a motor the 
greater will be this force or turning effort (torque), and con- 
sequently the greater the current taken by the motor arma- 
ture from the supply mains (Tl 314). 



Motion 




Fig. 323. — Single Loop Armature Driven as a Motor. 

284. Direction of Rotation of Motors. — The direction of 
rotation of a motor, or that in which any dynamo will rotate 
when used as a motor, can be found by the left-hand rule 
(^ 189) when the polarity of the field magnets and the direc- 
tion of current through the armature have been ascertained. 
Place the left hand, as shown in Fig. 323, so that the fingers 
correspond with the polarity and direction of current in the 
single armature coil motor, and it is found that the loop will 
rotate in the direction of. the hands of a clock. The direction 
of rotation of a motor can be changed by reversing the current 
either through the armature err through the fields, but not 
through both. If both are changed, the motor will run in 
the same direction as before. See H 191. 



388 LESSONS IN PRACTICAL ELECTRICITY 

Experiment 97. — Separately excite the field magnets of the student's 
experimental dynamo, Fig. 312; adjust the brushes so as to make contact 
with the collector rings; place the armature coil with its plane horizontal 
and pass a current through the armature. The coil is urged around 
until its plane becomes vertical, when rotation ceases, according to the 
principle outhned in *\ 283. Incline the coil at any angle to the vertical 
position, and upon closing the circuit it rotates to the vertical position 
and stops. 

Experiment 98. — Now adjust the brushes upon the two-part commutator 
and repeat Experiment 97. The coil rotates continuously in one direction, 
the direction of current being reversed by the commutator at each half 
revolution. 

Experiment 99. — Find the polarity of the field magnets with a compass, 
also the polarity of the supply Une, and note whether the direction of 
rotation is according to the left-hand rule. 



QUESTIONS 

1. How does a generator differ from a primary battery as a source 
of electricity? 

2. Classify dynamos according to their mechanical construction. 

3. How does an alternator differ from a direct-current generator? 

4. Why are large generators constructed with multipolar rather than 
bipolar fields? 

5. Sketch four positions of a single rectangular coil of wire at each 
quarter of a revolution in a bipolar field. Assuming the terminals of the 
coil to be provided with two collector rings, indicate polarities and direc- 
tion of the current in the internal and external circuits in each sketch. 

6. Make sketches when the terminals of the coil in Question 5 are 
connected to a two-part commutator. 

7. The armature of a generator revolving at 1000 revolutions per minute 
generates 110 volts. State two ways in which you can increase the voltage, 
using the same armature. 

8. State the operating principle of the direct- current motor. 



LESSON XXIV 

ARMATURES 

Gramme Ring Armature — Induced E. M. F. in a Ring Armature — Drum 
Armature — Open-Coil Armatures — Eddy-Current Loss — The Com- 
mutator and Brushes — Armature Core Insulation — Table XVIII — 
Armature Windings — Hysteresis Loss — Armature Reactions — The 
Act of Commutation of an Armature Coil — Improvements in Com- 
mutation — Causes of Sparking — Questions. 

285. — Gramme Ring Armature. — A four-coil direct-cur- 
rent Gramme ring armature is illustrated in Fig. 324. The 
ring is made of a number of laminated sheets of soft iron and 
the coils wound upon it. The ending of each coil is joined 
to the beginning of the adjacent coil, 
so that the winding forms a complete 
closed circuit, or the coils are all in 
series. At the junction of each coil 
with its neighbor a lead wire is run 
to a commutator section, so that in- 
stead of the two-part commutator of 
If 280 one with four sections is now 
used. As the number of coils is in- Fig. 324. — Four -coil 
creased the commutator sections are Gramme-ring Direct-cur- 

j -n u J. J • 1. i"ent Armature, 

mcreased, as will be noted m subse- 
quent figures. An eight-coil ring armature is depicted in Fig. 
325, rotating with the hands of a clock in a bipolar field. The 
connections are the same as those given above. The magnetic 
lines of force issuing from the N-pole flow through the upper 
and lower halves of the core to the S-pole; very few lines cross 
the air space inside the ring. The direction of current in the 
coils on the two vertical halves of the ring is indicated by 
arrows and is found by the right-hand rule, If 249. 

When the external circuit is closed the induced current 
flows in both halves of the winding toward the upper or posi- 
tive brush, and returns from the external circuit to the lower 

389 




390 



LESSONS IN PRACTICAL ELECTRICITY 



or negative brush, circulating up again through each half of 
the armature. The windings in the halves of the armature 

are in parallel with the 



brushes. As each coil 
passes from under the 
influence of the N-pole 
and comes into action 
under the S-pole, com- 
mutation takes place 
and the direction of cur- 
rent through it is re- 
versed, as will be seen 
by tracing the direction 
of the currents in the 
two upper coils, which 
carry currents opposed 




Fig. 325. — Eight-coil Gramme-ring Direct- 
current Generator Armature. 



to each other. The brush is located at this point of opposition 
and serves to conduct the 
current from both halves 
of the ring to the external 
circuit. The brushes rest- 
ing upon two adjacent bars 
will thus short-circuit each 
coil for an instant as it 
passes from pole to pole, 
and this short-circuiting 
should occur when there 
is little E. M. F. in the coil. 
The circulation of current 
through the windings of a 
ring armature rotating in 
a four-pole field is shown 
in Fig. 326. The direction 
of rotation is counter clock- 
wise, and the direction of 
current through the windings under any particular pole can 
be found by the right-hand rule. The currents in the wind- 
ings under the upper N- and S-poles are opposed to each other 
and flow to the external circuit by the + brush 1 and back 




Fig. 326. — Direction of Current 
through the Windings of a Multipolar 
Ring Armature of a Generator. 



ARMATURES 391 

to this half of the armature by - brushes 3 and 4. At the 
same instant the opposed currents in the lower windings flow 
to the external circuit by + brush 2 and return to the arma- 
ture through - brushes 3 and 4. The armature is thus divided 
into four circuits and four brushes are required and must be 
placed between the poles so as to short-circuit the coils as 
they pass through the neutral space. In this form of winding 
there is no difference of potential between the + brushes, so 
that they are connected in parallel, as are also the negative 
brushes, and then to the external circuit. In multipolar 
machines there are as many brushes as pole pieces,^ and all 
the + brushes are generally connected to one main generator 
cable, forming the + terminal of the machine, and likewise 
with the negative brushes. 

286. Induced E. M. F. in a Ring Armature. — The upper 
and lower coils in the right-hand half of the ring armature 
(Fig. 325) will have about the same E. M. F. induced in them, 
say 20 volts each, while the two coils between them will have 
a higher E. M. F. at the same instant, say 40 volts each, since 
they occupy nearly the position of the maximum rate of change 
of the lines threading through them. The total E. M, F. 
of this half of the ring, since these four coils are in series, will 
therefore be 20 + 40 + 40 + 20 or 120 volts, and since similar 
induction takes place in the other half of the ring at the same 
instant, there will be a total of 120 volts induced in it. The 
windings of- the two halves being in parallel, the E. M. F. at the 
brushes will also be 120 volts, just as though each half repre- 
sented a battery of 120 volts E. M. F. and the two batteries 
were placed in parallel. The current in the external circuit 
will be the sum of the currents in each half of the winding. 
If it is 10 amperes, 5 amperes will flow through each half of 
the ring. The addition of the E. M. F.'s in the coils, and the 
current flowing from them, may be understood from the fol- 
lowing battery analogy. In Fig. 327, eight batteries represent 

^ Since opposite commutator bars are of the same potential on this 
four-pole dynamo they may be joined by a cross-connecting wire and 
two brushes, as 2, and 4, dispensed with. This can only be done when 
there is an even number of coils. The armature is said to be " cross- 
connected," 



392 



LESSONS IN PRACTICAL ELECTRICITY 



the above armature coils and are connected 4 in series and 2 
groups in parallel. The E. M. F. of one group of batteries is the 

sum of the E. M. F.'s of the bat- 
teries connected in series in that 
group, or 20 + 40 + 40 + 20 = 120 
volts, and the E. M. F. of 2 groups 
in parallel is 120 volts. If 10 am- 
peres flow through the external cir- 
cuit, 5 amperes will flow through 
each group of batteries. 

By employing 8 coils on this 
ring armature the current is less 
pulsating than in the four-coil 
armature of Fig. 324. As the num- 
ber of armature coils is further 
increased, thp wave becomes more nearly a straight line, but 
there will always be a slight pulsation of the current. 




y/3 ^mnaros 



Fig. 327. — Battery Analogy 
of Induced E.M.F. in a Ring 
Armature. 



Problem 116. — The joint resistance of the two halves of an 8.-poIe 
ring armature is 0.5 ohm. This is called the armature resistance and 
would be measured between the brushes. ' What is the resistance of all 
the wire upon the armature? 

By Formula (32) R = J. R. x nq. 
Here J. R. = 0.5 ohm, nq = 2 halves in parallel, and therefore 
R = 0.5 X 2 = 1 ohm. 

This is the resistance of one-half the armature, therefore the total resis- 
tance of the wire upon 

//?K?/y-5-A V.M. 

Leads l-Ohm. 



it = 1 X 2 = 2 ohms. The 
total resistance of the 
armature winding is thus 
four times the joint re- 
sistance from brush to 
brush in this type of 
armature. 

Problem [117. — The 
resistance of the eight 




in.b Yoifs 



Oenerafor 
0.4 Ohm 



Lamp 
20 Ohms 



< — ■ 5.6 Amperes 



^ 



Fig. 328. — E.M.F. and P.D. of an Armature. 



coils, in series, upon the ring armature of Fig. 325 is 4 ohms; what is the 
armature resistance from brush to brush? 

The resistance of one-half of the armature is 4 -;- 2 = 2 ohms. The 
joint resistance of the two halves in parallel is, 



by Formula (30), J.R. 



R 
nq 



2 
= - = 1 ohm, 

2 



ARMATURES 393 

Problem 118. — The E. M. F. generated by the ring armature in Fig. 
325 is 120 volts, the resistance of the armature is 0.4 ohm, of an incandescent 
lamp connected to the brushes 20 ohms, and of the leads to the lamp 1 ohm. 
What current will the lamp receive? See Fig. 328. 

If R and r be respectively the external and internal resistance, then by 
E 120 

Formula (35) I = ^^ = 20 + 1 + 0.4 = ^'^ ^^P"^^"'' 

Problem 119. — What potential will a voltmeter indicate when placed 
across the brushes in Problem 118? See Fig. 328. 

Formula (28) E = I x R = 5.6 x (20 + 1) = 117.6 volts. 

The pressure required to send 5.6 amperes through the armature will 
be E = I X r = 5.6 X 0.4 = 2.4 volts, or 120 - 117.6 = 2.4 volts. 

By substituting a pair of collector rings for the commuta- 
tor, the ring armature of Fig. 325 will give an alternating cur- 
rent to the external circuit. The winding is the same, but 
only two lead wires are taken from the coils, at points diametri- 
cally opposite and connected one to each collector ring. With 
the increased number of coils the alternating E. M. F. is in- 
creased, since the E. M. F.'s in the coils at any instant are in 
unison. The commutator and collector rings may both be 
mounted on the same armature shaft, in which case the ma- 
chine will give either a direct or alternating current, or both, 
at the same time to two independent circuits. The dynamo 
would then be called a double-current generator. The collector 
rings would be connected to diametrically opposite sections of 
the commutator; for example, a and b in Fig. 325. 

287. Drum Armature. — In the ring armatures already 
considered the wire forming the coils is wound in and out 
around the core, as shown in Figs. 324 to 326. Only that part 
of the wire which is located on the periphery of the ring cuts 
the magnetic lines of force and is therefore active in developing 
E. M. F. That part of the wire is termed the active wire, 
while that on the ends and inside of the ring, which serves only 
to connect one active conductor to the next, is called the dead 
wire. 

In the drum armature both sides of each coil are made effect- 
ive in producing E. M. F. by placing them on the periphery, 
usually in slots in a cylindrical laminated iron core. In con- 
sequence drum armatures have a greater percentage of active 
wire and a lower PR loss than a ring armature of the same 




394 LESSONS IN PRACTICAL ELECTRICITY 

dimensions. The two coil sides are so located that when one 
side is under a N-pole the other will be under the next adjacent 
S-pole. In a bipolar field this means that the coil sides are 
about diametrically opposite, as shown in Fig. 329, while in 
a four-pole machine each armature coil subtends one-quarter of 

the surface between its two sides, 
etc. The electromotive forces 
induced in the two sides of a coil 
will then be cumulative, that is 
the two E. M. F.'s will be in 
series. In practice a great many 
coils are placed on the core, 
covering its entire surface, the 
number of commutator segments 
incresaing with the sub-division 
of the armature winding. 

Both halves of the drum arma- 
Fig. 329. — Four-coil Drum ture coils are in parallel so that 
Armature. ^^^ induced E. M. F. of the ma- 

chine is that generated by one-half of the total conductors upon 
the core, and each half of the windings deliver one-half of the 
total current flowing to the external circuit. Drum armatures 
are used almost to the exclusion of the ring type. 

There is no necessity in drum armatures for employing 
solid cylindrical cores except in armatures of small diameter. 
In larger armatures the laminated core need only extend 
inward back of the winding slots to an extent allowing suf- 
ficient iron cross section for the magnetic lines of force. Such 
cores are assembled on a mechanical support, called a spider, 
which is later mounted on the shaft (Fig. 330). This con- 
struction affords splendid cooling facilities, and is economical 
in iron. While its general form is that of a ring, drum arma- 
ture cores of such construction should not be confused with 
the practically little-used ring armature. 

Fig. 330 depicts a drum armature of an Allis-Chalmers gen- 
erator, having its core built up from punchings of thin sheet 
steel and held in position by two rings securely fastened 
to the spider arms. The coils are first wound, then properly 
shaped upon formers, removed, wrapped with insulation, 



ARMATURES 



395 



varnished and baked to expel all moisture, and then placed 
in the slots of the armature core. The winding is held in place 
by retaining wedges and the end connections are held by band- 
ing wire. The coil terminals are properly connected to the 
commutator. In some types of large size generators, solid 
copper bars, properly insulated, varnished, baked, etc., are 
placed in the armature slots, which are lined with mica formed 




Fig. 330. — Armature and Commutator Mounted on 
Spider or Quill. 

tubes. The bars are then connected by flexible formed ter- 
minals, according to the method of winding. 

288. Open-Coil Armatures. — The armatures previously 
described are called closed-coil armatures, because the coils are 
all connected to form a closed winding around the armature. 
Generators for series constant-current, street-lighting circuits, 
which were formerly used to a large extent, were generally 
equipped with open-coil armatures. A simple ring armature 
of this type is depicted in Fig. 331. Two coils, A and B, 
wound at opposite positions on the ring core, are connected 



396 



LESSONS IN PRACTICAL ELECTRICITY 




Fig. 331. — Open-coil 
Armature. 



in series to two diametrically opposite commutator bars, 1 and 
2. Another pair of coils, C and D, is wound in a position at 
right angles to the former coils, and the two coils are cbn- 
nected in series to two independent diametrically opposite bars, 

3 and 4. At a particular instant 
during the revolution, shown in 
Fig. 331, the coils C and D have 
the maximum E. M. F. induced in 
them, and are connected to the 
external circuit by the brushes, 
while coils A and B are in the posi- 
tion of zero induction and out of 
circuit at this instant. An instant 
later coils A and B will be in the 
active position and connected to 
the circuit while coils C and D are 
cut out. Two independent two-part commutators are used 
instead of that shown and placed side by side, one set over- 
lapping the other. By making the brush equal to the width of 
both sets of bars, the 
external circuit is not 
broken each time a pair 
of coils is switched 
out of circuit. With 
the four-coil armature 
the current would be 
very pulsating in the 
external circuit, so that 
more coils are used with 
correspondingly more 
commutator segments, 
or several commutators 
placed side by side on a 

shaft, and their respective brushes connected in series or parallel 
with the external circuit. 

289. Eddy Current Loss. — The armature core which is in- 
troduced into the magnetic circuit of a dynamo to lower its 
reluctance is an electrical conductor also, and when rotated in 
the magnetic field will have currents induced in it, according to 




Fig. 332. — Eddy Currents in the 
Armature Core. 



ARMATURES 



397 




Fig. 333. — Sheet Iron 
Armature Lamination. 



the principles of electromagnetic induction. A certain portion 
of the energy driving the armature is thus expended in pro- 
ducing useless electric currents, eddy currents (U 254), in the core 
and which do not appear in the ex- 
ternal circuit; this is termed eddy 
current loss, and constitutes one of 
the internal losses of a dynamo. A 
section of a solid armature core is 
illustrated in Fig. 332, and the direc- 
tion of the induced eddy currents, 
as determined by the right-hand 
rule (^ 249), is indicated. The flow 
of these currents represents a waste 
of energy appearing as heat in the 
core. The armature wires being 
wound on the core will also be 
heated and their resistance increased, and as a result the PR 
loss will be raised. 

Eddy current losses may be considerably diminished by build- 
ing up the armature of 
a series of thin disks of 
soft sheet iron or steel, 
the surfaces of which 
have been allowed to 
oxidize (rust), thus in- 
troducing an insulator 
between the sheets, 
which decreases the 
electrical conductivity 
of the core. Sometimes 
pieces of tissue paper or 
coats of insulating var- 
nish are interposed be- 
tween the sheets to 
break the continuity of the electric circuit. A single sheet iron 
punching of a tooth-core armature is represented in I'ig. 333, 
while the effect of lamination is shown in Fig. 334, in which the 
eddy currents are confined to each lamination. By laminating 
armature cores in this way the resistance of the entire path of 




Fig. 334. — Laminated Armature Core. 

The thickness of disks is magnified to show the 
eddy currents. 



398 LESSONS IN PRACTICAL ELECTRICITY 

eddy currents is greatly increased and therefore the strength of 
these currents diminished. The eddy current loss in the 4-disk 
core of Fig. 334 is only Jg of that in the soHd core of Fig. 332 
for otherwise identical conditions. To reduce this loss still 
further a great many disks are used for a single armature core; 
indeed, the thickness of the metal from which laminations are 
punched may be as small as 0.014 inch. 

290. The Commutator and Brushes. — A commutator con- 
sists of a number of bars or segments of drop-forged or hard- 



MrCA COLLAR EXTENDS 



JOINT iHERE MADE OIL-TIGHT 
■■WITH OIL- PROOF COMPOUND 




LARGE SOLID RISERS 



COMMUTATOR SLEEVE 



uorroM OF bar js rounded 



Fig. 335. — Sectional View of Commutator. 

Made by Reliance Electric & Engineering Co, V 

drawn copper, assembled around an iron hub and thoroughly 
insulated from the hub and from each other (P'ig. 335). Mica 
is used for the insulation, its thickness usually varying from 
0.02 to 0.15 inch, depending upon the voltage of the machine. 
The bars must be securely held in place, since a high or low 
bar would cause a break in the circuit each time it passed under 
the brush and destructive arcing would result. 

In the construction of a corn mutator, the segments and 
mica strips are assembled and clamped firmly together by an 
external temporary steel ring. Grooves are then turned into 
the inner surface to fit the commutator sleeve and the clamping 
ring, as illustrated in Fig. 335, and thereafter the various 



ARMATURES 



399 



parts are securely clamped together by cap screws. The 
external steel ring is now removed and the outside surface of 
the commutator is machined into a true cylinder. The manner 
of locking the commutator bars without short-circuiting them 




Fig. 336. — Armature for " Peerless " Motor. 

At each end is shown a bearing with its oil rings. 

will be understood from an inspection of Fig. 335. A lug or- 
riser extends at right angles from one end of each bar to which 
the armature lead is soldered. Fig. 336 shows the completed 
armature. 

The current is conducted to and from the armature by 
means of brushes which are guided 
by brush holders and made to press 
against the commutator by spring 
pressure. Brush holders should be 
carefully designed so as to avoid 
vibration of the brushes, a common 
cause of sparking. Details of a brush 
holder are shown in Fig. 337. The 
brush holder stud or shaft is securely 
bolted to, but insulated from, the 
rocker arm or brush holder yoke, and 
connected by flexible cables to the external circuit. The func- 
tion of the rocker arm is to move the position of the brushes 
upon the commutator so that the current is led to and from 




Fig. 337. — Brush Holder 
(General Electric Co.) 

Brush slides freely in holder. Con- 
nection is made by stranded copper 
wire called a pigtail. 



400 



LESSONS IN PRACTICAL ELECTRICITY 




Fig. 338. — Commutator End of Large Engine-driven Generator. 

Allis-Chalmers 2000-kw., 250-volt, 90-rev. per min. generator. 

the armature at the proper points of commutation. Fig. 338 
shows the commutator end of a large AlHs-Chalmers generator, 
and illustrates the method of supporting the numerous brushes 
on a slow-speed multipolar machine. 

Brushes are generally made of hard graphitic carbon, al- 
though in low-voltage dynamos brushes of copper gauze are 



ARMATURES 



401 



used to advantage because of their lower resistance. Copper 
brushes are also used in some turbine-driven generators. 

291. Armature Core Insulation. — The armature cores of 
generators are slotted for the reception of the conductors, 
which must be thoroughly insulated from the core. Windings 
may be insulated with micanite, pressboard, paper, cotton, var- 
nished cloth, etc., the amount and quality depending upon the 
potential to be developed by the armature; an armature 
wound to develop 1000 volts requiring a better grade of in- 
sulation than one wound for only 125 volts. 

The quality of an insulating material is tested by subjecting 
it to a high potential and ascertaining at what voltage the' 
insulation " breaks down," or conducts, instead of insulates. 
The specimen to be tested, as a piece of paper or fiber, may 
be interposed between two plates connected to a source of 
high potential, which is capable of being regulated. The 
voltage is then increased till a spark passes from plate to 
plate through the specimen, thereby puncturing it. The fol- 
lowing insulating materials and the voltages at which they 
" broke down " under test will give the student some idea of 
what is meant by insulating quality. 

Table XVIII. Insulation Test 





Thickness 


"Break down" 


Material 


in inches 


voltage 


dry cotton tape 


0.013 


250 


soft gray wrapping paper 


0.010 


1,000 


asbestos paper 


0.015 


1,500 


varnished cloth 


0.010 


7,500 


red sheet fiber 


0.037 


7,000 


press board or fuller board 


0.022 


5,000 


micanite 


0.018 


14,000 



The insulation of electrical machinery is usually tested by 
applying a greater voltage than the apparatus is designed to 
stand; for example, a 1000- volt armature may be subjected 
to 3000 volts, one terminal of the high potential source being 
connected to the core, and the other to the copper windings. 



402 



LESSONS IN PRACTICAL ELECTRICITY 



The standard test voltage for many classes of apparatus is 
twice the normal voltage of the circuit to which the apparatus 
is connected, plus 1000 volts. If there is any defect in the 
insulation, upon application of the high voltage it will readily 
be noted on indicating instruments in the testing circuit. 

In large machines the conductors are generally in the form 
of straight bars of rectangular cross section which have been 
previously insulated. One or more bars are inserted in each 



leads robe attached 
to cofnmutator bars. 



Treated duck strips protect 
coils from rubbm?. 



fi5h paper cells protect 
coils in core slots. 




i Coils fit compactly with 
( flat sides together. 



Artnature keyed to shaft which may be 
removed withouf disturbing windings. 



End-plate 
riveted to core. 



Fig. 339. 



Partly-wound Armature Showing Method of 
Assembling Coils. 



slot, and the coils formed by connecting their ends to other 
bars by flexible formed end terminals soldered to them, pro- 
vision being made for commutator taps at the ends of the 
proper coils, when the armature is for a direct-current machine. 
It is not advisable to use bars of very large cross section 
because of the eddy currents set up in them when one side of 
a conductor happens momentarily to be in a stronger field than 
the other. Instead it is best to use several smaller conductors 
of equivalent total cross section and connected in parallel at 
the commutator. 



ARMATURES 



403 




Fig. 340. — Position of a Coil on a Bipolar 
Drum Armature. 



In medium sized multipolar machines the windings con- 
sist of a number of formed coils, each coil being composed 
of several conductors of round or rectangular wire individually 
insulated and then 
fastened together with 
cotton, linen or var- 
nished cloth tape. 
Such formed coils pos- 
sess superior insulation 
and permit of speedy 
removal in case of repair 
without disturbing ad- 
jacent coils. Fig. 339 
illustrates the method 
of assembling the 
formed coils of an arma- 
ture of a type SK West- 
inghouse motor. 

292. Armature Windings. — The coils of an armature may 
be connected to each other and to the commutator segments 
in a variety of ways that will yield satisfactory operation. 

Practical armature windings are eco- 
nomical in copper, render satisfactory 
commutation, and are accessible for 
making repairs. Present windings are 
designated as single or multiplex wind- 
ings, two-circuit (wave) or multiple- 
circuit (lap) windings, etc.^ 

A small drum armature for a bipolar 
field is shown in Figs. 340 to 342. 
Suppose it is to be wound as a closed- 
coil armature with 8 coils and 3 turns 
per coil. The armature core would 
have 16 slots and the first coil wound 
in slots 1 and 9; the second in 2 and 10, and so on. Com- 
mence to wind the beginning of coil No. 1 in slot 1; and its third 
turn will end in slot 9, Fig. 340; commence coil No. 2 in slot 2, 
wind in the same direction as the first and it will end in slot 10, 
^ Armature winding is treated in books relating to dynamo design. 




Fig. 341. — Connecting 
the Armature Coils to the 
Commutator. 



404 



LESSONS IN PRACTICAL ELECTRICITY 



and so on. The coils should then be bound to the armature 
core by mounting it in a lathe and winding several bands around 
it, each consisting of a number of turns of phosphor bronze wire, 
soldered together. A commutator with 8 bars will be required 
since there are 8 coils and the coils are to be joined in series. 
Connect the beginning of coil No. 1 to bar 1 and the ending of 
coil No. 1 to bar 2, Fig. 341; the beginning of coil No. 2 to the 
ending of coil No. 1 at bar 2; the ending of coil No. 2 to bar 3 
and to the beginning of coil No. 3, and so on until finally the 



Coils 




a □ □ 

3-456 
Commufafor Segments 



7 



Fig. 342. — Developed Bipolar Armature Winding. 

ending of coil No. 8 will connect to the beginning of coil No. 
1 at bar 1. The coils are thus all in series around the arma- 
ture, the commutator bars forming the connecting links be- 
tween the coils. Fig. 342 shows the same winding developed, 
that is the armature and commutator surfaces are rolled out 
flat; such diagrams are often used. 

Many more turns could be wound per coil in order to increase 
the induced E. M. F. After the first set of coils is wound a 
second set may be wound on top of them, with proper insulation 
in the slots between them; 16 commutator bars would have 
been required had this method been adopted in Fig. 341. 
There would then be two coil sides a and b in each slot, as 
shown at B in Fig. 343. The method of varying the winding 



ARMATURES 



405 



according to the potential desired is illustrated in Fig. 343, 
which represents the number of wires per slot on a 5-kw. 
dynamo when it is wound for 125 volts, as in A; 250 volts, in 
B; 500 volts, in C. The size of the wires decreases as the 
voltage increases, since for the same power the current will 
be less, and the turns increase in direct proportion to the 
voltage, there being 3, 6 and 12 turns per coil to correspond 
with 125, 250 and 500 volts. The speed and field strength are 
assumed the same for each armature. . 



Op 

qo 
do 



oonoo 
oooo 
ooUoo 


a 
b 



OOOO 

oooo 
oooo 



Fig. 343. — Windings of a 5-kw. Armature. 

125 volts. B — 250 volts. C - 



500 volts. 



The following illustration will give the student some details 
of a direct-current generator armature. 

Rating: 400 kw., 240 volts, 10 poles, 200 rev. per min. 
Core: 58 in. diameter, 12 in. long, 200 slots 1.6 in. deep and 

0.43 in. wide. 
Winding: 1-turn multiple winding having 4 conductors per 

slot, section of conductor 0.55 X 0.14 in. 
Commutator: 32 in. diameter, 13 in. long, 400 segments. 

293. Hysteresis Loss. — The iron core of a drum armature 
rotating in a two-pole field will be subjected to two opposite 
magnetic inductions in each revolution. For example, consider 
the polarity of the core at one instant during its revolution 
(Fig. 344) ; the left-hand side of the core has a S-pole induced 
in it by the N-pole of the field magnet, while the right-hand 
side of the core possesses an induced N-pole from the S-pole 
of the field magnet at the same instant. After one half revo- 
lution of the core from this point that part which previously 
possessed induced N-polarity is now inductively magnetized 
with a S-pole, and the other half with a N-pole. The core is 
thus subjected to two opposite magnetizations in each revolu- 
tion. Suppose the speed to be 2000 revolutions per minute, 



406 



LESSONS IN PRACTICAL ELECTRICITY 




Fig. 344. — Armature Core Loss 
due to Hysteresis. 



then there will be 4000 reversals of magnetization per minute 
in the core. This reversal involves molecular friction, called 
hysteresis, and causes the development of heat (^ 255, Ex- 
periment 88). A portion of 
the energy required to drive 
the armature is thus expended 
in heating the core and does 
not appear as useful electrical 
work. The heat so generated 
also heats the copper wires 
wound upon the armature 
core, increasing their resistance 
and the PR loss, so that still 
more energy is wasted which 
does not appear as useful 
energy. This hysteresis loss, together with the eddy-current 
loss (1[ 289), constitutes the core loss in a dynamo. 

294. Armature Reactions. — The current flowing from a 
generator armature circulates through its internal windings, 
and produces magnetic poles in the armature core which react 
upon the magnetic field, 
which produced the armature 
current. If a current be 
sent from some outside source 
through this armature with 
its own field magnets unener- 
gized, it would set up a mag- 
netic field, as illustrated in 
Fig. 345. The conductors 
are here shown on the surface 
of the armature with the cur- 
rent flowing toward the ob- 
server in the left-hand con- 
ductors and away from him 
in the right-hand conductors. It is seen that the axis of this 
field N-S is across that of the main field, as shown in Fig. 344, 
and is therefore termed cross flux. 

In the operation of this armature as a generator both the 
main field and cross field exist at the same time, and the entire 




-Magnetic Field Pro- 
duced by Current Circulating through 
the Armature. 



ARMATURES 



407 




Fig. 346. — Distortion of the Mag- 
netic Field due to the Cross-magnet- 
izing Effect of the Armature Current. 



field is obtained by combining Figs. 344 and 345, with the 
result shown in Fig. 346. 

In the upper half of the right pole piece the direction of 
the cross flux (Fig. 345) is the same as that of the main field 
(Fig. 344) consequently the 
resultant flux there is intense; 
whereas in the lower half of 
that field pole the two fluxes 
are opposed and the result is 
a weak field. These condi- 
tions are represented in Fig. 
346 by the closeness of the 
lines of force. The distribu- 
tion of these lines through 
the generator field poles and 
armature is therefore non- 
uniform, or the main field is said to be distorted by the armature 
flux. 

The position of maximum induction then is not along the 
horizontal line, as considered in the ideal dynamo (^ 276) 

but along a line inclined at 
an angle to it, the angle in- 
creasing as the current from 
the armature increases. As 
a result of this field distor- 
tion the position of mini- 
mum inductive action in the 
armature coils will not be 
along the vertical line 
marked neutral plane in Fig. 
347, but along a line some- 
what in advance of it, in the 
direction of the armature 
rotation, as the line ab, 
which is perpendicular to the resultant flux axis of Fig. 346. 
Commutation of an armature coil should therefore take place 
as the coil passes the line ab, which is therefore called the com- 
mutating plane. The brushes should be set at diametrically 
opposite points (in a bipolar dynamo) and then shifted to a 




P/ane 



Commufaffnq 
Plane 



Fig. 347. — Shifting Brushes from 
Neutral Plane because of Armature 
Reaction. 



408 



LESSONS IN PRACTICAL ELECTRICITY 



position corresponding to the commutating line. The angle 
of advance of this line from the vertical position will depend 
upon the current flowing from the armature (the field dis- 
tortion increasing with the current), being shifted forward 
for an increase, and backward for a decrease in the armature 
current. The brushes must therefore be shifted forward in 
the direction of rotation for an increase of current from the 
machine, and backward for a decrease. When the brushes 
are not set to correspond with the commutating plane, spark- 
ing at the brushes may result. 

295. The Act of Commutation of an Armature Coil — 
Sparking at the Brushes. — The act of commutation of an 

armature coil, that is, its 
passage from under the 
influence of one pole to go 
under that of the other, 
is illustrated in Fig. 348. 
For an instant, each coil 
is completely short-cir- 
cuited by the brush, and 
during that time the cur- 
rent that was flowing in it 
must be reduced to zero 
and brought up again to 
full value in the opposite 
direction. While at the 
point A (Fig. 348), a 
definite amount of magnetic flux encircles the coil because of 
the current in it. This flux should consequently disappear and 
be reestablished in the reverse direction before the coil is trans- 
ferred to the other side of the brush at C. It was pointed out 
in ^ 257 that when the flux surrounding a coil due to its own 
current is varied, an electromotive force is induced which is 
called an E. M. F. of self-induction. Likewise, in the armature 
coil undergoing commutation, the changing flux develops an 
E. M. F. of self-induction, which in this case is commonly called 
reactance voltage. The presence of this voltage in the short-cir- 
cuited coil is undesirable, for suppose its value at a particular 
moment to be 1 volt, then the current circulating through that 




Fig. 348. — The Act of Commutation 
of an Armature Coil. 

At the instant shown coil B is short-circuited 
by the brush. 



ARMATURES 409 

coil and the toe of the brush which together, may have a re- 

E 1 

sistance of say 0.01 ohm, would be I = — = — — - = 100 amperes. 

IX 0.01 

This current flow through a short-circuited coil may be 
reduced by the introduction of (1) resistance in the coil cir- 
cuit, or (2) an opposing E. M. F. into the coil at the time of 
commutation. Resistance increase is usually affected by the 
use of carbon brushes rather than of high-resistance leads 
from armature winding to commutator, and an opposing 
E. M. F. may be obtained by so placing the brushes that the 
coil will cut a small amount of flux from that field magnet 
pole toward which the coil is moving. That is, the plane of 
commutation is shifted so that the coil, while short-circuited 
at a brush, will pass through a magnetic field of opposite 
direction of such strength that an E. M. F. will be induced 
in the coil sufficient to reverse the direction of the initial cur- 
rent in spite of the reactance voltage, which is developed by the 
varying flux due to the changing current in the coil. If the 
current strength in the coil after reversal is identical with 
its original intensity, then the coil may be transferred to the 
other side of the brush without disturbance, and sparkless 
commutation will be achieved. In practice, to find the non- 
sparking brush-position of a generator when it is running, the 
brushes are rocked backward or forward _ , 

until the sparking practically disappears, ^ ^j j ^^^ 
or until a point is found where it becomes C^U^S^^^^ 
a minimum. ^^^^ ^a^^"---' 

The tendency of a dynamo to spark ^-I^^^ ^K^^^-^ 

can be greatly reduced if, in construe- "^^rrTW!^^ 

tion, the armature is divided up into j !3 "^ 

many coils. Each coil will then have Q4q_c;viff 

relatively few turns, and its inductance PosHion of the BruSfes. ^ 
and therefore its reactance voltage will i — Fuiiioad 2— Half load. 
be small (the inductance of a coil is pro- 3 — No bad. 

portional to the square of the number of its turns. Formula 98). 
The reactance voltage of modern dynamos seldom exceeds 3 
volts per segment, and splendid commutation is obtained. 

Many dynamos, however, do spark at the brushes, but the 



410 



LESSONS IN PRACTICAL ELECTRICITY 



fault lies in the manner of adjusting the brushes, etc., rather 
than in the design of the machine. Some of the causes of 
sparking are given in 1| 297. 

The greater the current output of a machine the greater 
must be the E. M. F. induced in the short-circuited coil to effect 
the reversal of its current. This means that with increasing 
load the coil undergoing commutation must be brought into 
a more intense field. This is accomplished in older machines 
by shifting the brushes. In Fig. 349 is shown somewhat ex- 




Fig. 350. — Field Frame of a 150-kw. Generator. 

Illustrates brush shifting mechanism. 

aggerated the relative positions of the brushes of a 2-pole gener- 
ator running at: 1st, full load; 2d, half load; 3d, no load. The 
brushes are therefore gradually advanced from position 3 to 
position 1 as 'the machine is loaded, and likewise rocked back- 
ward from 1 to 3 as the load is diminished. The shafts which 
hold the brushes are attached to a cradle or arm, which can be 
moved to properly shift the brushes. Fig. 350 shows the shift- 
ing device used in an engine-type generator. 

296. Improvements in Commutation. — It will be remem- 
bered from U 294 that the current in the armature of a dynamo 
is responsible for the cross flux which produced distortion of 
the magnetic field and necessitated a shift of the brush axis. 



ARMATURES 



411 



If the magnetomotive force which sets up this cross flux were 
always neutralized by an equal amount oppositely directed, 
then there would be no transverse flux, and shifting of the 
brushes would be unnecessary when the load on the machine 




Fig. 351. — Field Frame of a Generator Showing Com- 
pensating Winding. 

Outer coils constitute the main field winding, inner coils comprise 
the compensating winding. 

changes. This compensating magnetomotive force should 
preferably be provided in such a manner that the armature 
coils undergoing commutation would have E. M. F.'s induced 
in them which would balance the reactance voltage (If 295) 
at all loads and reverse the direction of current in these coils. 
Then the brushes might be permanently and centrally located 



412 



LESSONS IN PRACTICAL ELECTRICITY 



for all loads and for either direction of rotation, with satisfactory 
commutation. 

The compensating magnetomotive force above mentioned 
may be provided by a winding embedded in slots in the field 
poles through which the armature current is passed. This 

construction is illustrated 
in Fig. 351, which shows 
the field frame of a 250- 
kw., 16-pole generator 
made by the Ridgway 
Dynamo and Engine Co. 
The field poles and yoke 
are entirely of laminated 
steel, and the compensat- 
ing winding occupies slots 
in the pole faces. 

The use of auxiliary 
poles between the main 
field poles of dynamos is 
effective in reducing arma- 
ture reaction by producing 
a magnetomotive force 
approximately balancing 
that of the armature. 
These poles are called 
inter-poles or commutating 
poles, and provide in the region between the main poles a field 
of such strength and direction as will set up the proper E. M. F. 
in the coils undergoing commutation for the reversal of current. 
The coils on the interpoles are traversed by the entire arma- 
ture current, or by a definite part of it. The field structure 
of a dynamo with commutating poles, manufactured by the 
Electro Dynamic Co., is shown in Fig. 352. Interpoles are 
especially used on shunt motors for variable speed service and 
in series motors for railways. 

The General Electric Co. in its Type RF adustable speed 
motors utilizes both the compensating winding and interpoles. 
Fig. 353 shows the field frame of a 4-pole motor of this type 
with and without the coils assembled. Successful commu- 




Fig. 352. — Field Frame of Interpole 
Motor. 

Shows relative position of main (large) and 
commutating poles. 



ARMATURES 413 

tation of high peak loads at any speed within a range of 100% 
to 400% of its minimum speed in either direction is claimed 
for this motor. 

297. Causes of Sparking. — In properly designed and con- 
structed dynamos, sparking may ensue because: 

1. Brushes are not set at the commutating plane. They 
should be rocked until this position is found. Brushes should 




Fig. 353. — Frame of Compensated Interpole Motor. 

Showing construction of main and Showing compensating coils embedded in 

interpoles. main poles and the other coils in place. 

be accurately and equally spaced on' the commutator so that 
they have the same number of commutator bars between 
them. 

2. Brushes are set with insufficient pressure against the 
commutator. 

3. Brushes are not set to obtain the full area of contact 
with the commutator. 

4. Brushes vibrate or chatter. 

5. A high, low, or loose commutator bar causes poor con- 
tact with the brush. 

6. Loose connection exists between armature coil and com- 
mutator bar. This will be noted by a peculiar blue snappy 
spark just as this particular bar passes under the brush. 

7. Commutator is worn in ridges, causing an uneven sur- 
face for brush contact. 



414 LESSONS IN PRACTICAL ELECTRICITY' 

8. Armature section is either short-circuited by a breakdown 
in the insulation or open-circuited in the winding. If the 
machine can be stopped for a short time this coil should be 
disconnected, its ends taped, and a wire of the same size as 
that used in the armature used as a bridge to connect the com- 
mutator bars formerly connected to the detached coil. The 
continuity of the armature circuit will thus be maintained 
and the machine can be run until the coil can be rewound. 

9. Overload on the dynamo. This will be noted by the 
ammeter in the circuit, also by the sparldng of the brushes 
and the increased temperature rise of the machine. 

10. Collection of dirt and grease on the commutator, which 
assists in preventing a good brush contact. Carbon or copper 
particles may short-circuit some commutator segments. The 
commutator must be kept clean. 

QUESTIONS 

1. What is the difference (a) between a drum and a ring armature? 
(b) between a closed-coil and an open-coil armature? 

2. Make a sketch of a 12-coil direct-current bipolar ring armature 
with two turns per coil; indicate the direction of current in the armature 
coils and in the external circuit. 

3. The resistance of all the wire wound upon a bipolar armature is 
2 ohms. What is the armature resistance? Ans. 0.5 ohm, 

4. The armature in Ques.tion 3 generates an E. M. F. of 50 volts. 
What current will flow through some lamps joined in parallel with it if the 
lamps have a joint resistance of 4 ohms; resistance of lead wires is 1 ohm? 
Ans. 9.1 amperes. 

5. What will be the P. D. indicated by a voltmeter, in Question 4, 
when placed (1) across the lamps? (2) across the brushes? Ans. (1) 36.4 
volts; (2) 45.5 volts. 

6. What is meant by laminating an armature core? Why is this 
essary? 

7. State three ways in which energy is uselessly expended in the arma- 
ture of a dynamo. 

8. What is the neutral plane and the commutating plane of a dynamo? 

9. Locate the proper positions of the brushes in a bipolar generator 
when the armature rotates against the hands of a clock. 

10. Why should a coil be commutated as it passes through the com- 
mutating plane? 

11. Since a two-part commutator is so simple in construction, why 
are armature windings subdivided into many coils, thus necessitating 
many commutator bars? 



ARMATURES 415 

12. In some generators it is necessary to change the position of brushes 
for changes in the current flowing from the machine. Why is this? 

13. What is the total output current of the 400-kw. armature 
described in *II 292 ? How much current does each conductor carry ? 
Ans. 1670 amps.; 167 amps. 

14. A piece of mica subjected to an insulation test is said to have 
broken down at 4500 volts. What is meant by this? 

15. An armature contains a defective coil. How would you tem- 
porarily remedy the trouble so that the machine could be operated? 

16. What is the function of interpoles or compensating windings in 
a generator field? 

17. State some causes for sparking at the brushes of a dynamo. 



LESSON XXV 

DIRECT-CURRENT GENERATORS 

Classification of Dynamos according to their Field Excitation — The 
Self-exciting Principle of Direct-Current Generators — Residual 
Volts — The Shunt Generator — Action of the Shunt Generator — 
Action of the Series Generator — Compound Machines — Compound- 
wound Generators in Parallel — Three-Wire Generators — Capacity 
of a Generator — Commercial Rating of Generators — Losses in a 
Dynamo — Efficiency of a Generator — Questions and Problems. 

298. Classification of Dynamos according to their Field 
Excitation. — The current for magnetizing the field magnets of 
a generator may be supplied from a separate generator or by 
the machine itself, it would be styled respective!}^ a separately- 
excited or a self-exciting generator. The methods of excitation 
are, of course, independent of the field construction and depend 
only upon the windings and their connections. Generators may 
be classified according to the methods used to excite the field 
magnets as follows: 

(a) Magneto Machines (Fig. 317). — The field magnets are 
permanent magnets of horseshoe form and the armature is 
designed for either direct or alternating current. Such ma- 
chines supply limited power and are used chiefly in gasoline 
engine ignition work, telephone signaling, and testing of 
circuits. 

1. Direct-Current Machines. — 

(b) Series Machines (Fig. -354) {Constant Current). — The 
field magnets are connected in series with the armature and 
wound with a few turns of heavy wire having a low resis- 
tance, so as to present little opposition to the main current 
flowing through them. Series generators are only used for 
series street-lighting circuits (T[ 288) and in the Thury system 
of high-voltage direct-current power transmission. 

41fi 



Series Field 




Ex+ernal Circui-/- 

wwwww 

354. 




rxferna I Circuit 

vwwv 

356. 

Series 
Field 




Fxfernal CIrcuif i 

\A/VWVW 

358. 




Extern a I Circuif \ 

WWW 



Shunt Field 




External Circuit 

\AA/WVVW 

355. 



Shunt 




External Circuit 




Extern a I Circuit 

vwww 

359. 




360. 
Figs. 354-361. — Classification of Generators according to the Method 
of Exciting the Field Magnets. 



418 LESSONS IN PRACTICAL ELECTRICITY 

In a constant-current circuit supplied by a series generator the 
current is maintained constant through the external circuit, 
while the E. M. F. varies with each change in the resistance 
of the circuit. Street arc or incandescent lamps, when oper- 
ated in series from constant-current machines, usually carry 
6.6, 7.5 or 9.6 amperes and the voltage may vary from 45 to 
8000 volts, according to the number of lamps in circuit. The 
reason for operating these lamps in series is that they are 
generally distributed over a very large area, and an economy 
in copper is effected by employing a small wire, generally about 
No. 6, for the series circuit and using a high voltage. The 
direct constant-current system of street lighting is now little 
used. 

(c) Shunt Machines (Fig. 355) {Constant Potential). — The 
field magnets are connected in parallel or shunt with the 
armature and are wound with many turns of small wire; they 
have a high resistance, compared with the armature, since only 
a small portion of the main current need flow through them. 

(d) Separately- Excited Machines (Figs. 356 and 357) (Con- 
stant Potential) . — Current for the field magnets is supplied 
from a separate generator. In Fig. 356 this generator forms a 
part of the main machine by having a, separate armature on 
the same shaft, while in Fig. 357 the field is supplied by a dis- 
tinct machine called an exciter. 

(e) Compound Short-shunt Machines (Fig. 358) {Constant 
Potential). — The field cores contain two independent spools. 
One is wound with a few turns of heavy wire, forming the 
series coil, and connected in series with the main circuit; 
the other, with a great many turns of smaller wire, forming 
the shunt coil, and connected in shunt with the armature. 

(f) Compound Long-shunt Machines (Fig. 359) {Constant 
Potential) . — The same as (e) except that the shunt field 
bridges not only the armature but also the series field; hence 
it is called a long shunt, 

2. Altemating-Gurrent Machines. — 

(g) Separately-excited Machines (Figs. 356 and 357). — 
The field magnets are excited from an auxiliary generator (or 
exciter). Alternators require an exciter, since the alternating 



DIRECT-CURRENT^ GENERATORS 419 

current cannot be employed to excite the fields. The exciter 
may be either a separate generator or an independent direct- 
current winding upon the alternator shaft, thus rendering the 
machine self-contained. Fig. 362 illustrates a 50-kw. engine- 
driven alternator, with its exciter direct-connected to the shaft, 
(h) Compound Separately-excited Machines (Fig. 360) . — 
Two independent field windings correspond to the series and 
shunt coils of Fig. 358. The shunt coil is supplied from an 




Fig. 362. — Alternator with Direct-connected Exciter. 

exciter, while the main current, commuted, flows through the 
series field coils. This method is employed in composite- 
wound alternators, a portion of the main alternating current is 
commuted by a special device called a rectifier, located on the 
armature shaft. Its function is to change that portion of the 
alternating current intended for the series coils into a direct 
current for producing the magnetization. A self-contained com- 
posite-wound alternator is depicted in Fig. 361. 

The field circuit of all dynamos except those of small size 
should not be broken . suddenly , because the voltage of self- 
induction may rise to such value as to injure the insulation 
(see Experiment 90). A discharge resistance and special field 



420 LESSONS IN PRACTICAL ELECTRICITY 

switch are generally used, the magnetic energy of the field being 
converted into heat in the resistance. 

299. The Self-exciting Principle of Direct-Current Gen- 
erators — Residual Volts. — If the soft iron or steel field 
cores of a generator have once been magnetized they retain 
permanently a small amount of their magnetism. An arma- 
ture revolving in even so weak a field as that due to residual 
magnetism will cut some lines of force, and as a result there 
is an E. M. F. maintained at the brushes without any excita- 
tion. This is often spoken of as the residual volts, and will 
be indicated upon a voltmeter connected to the brushes, when 
the field circuit is open, and the armature revolves at its proper 
speed. This E. M. F. may be from 2 to 10 volts or more, 
depending upon the quality of the iron, the number of armature 
conductors, etc. If now the field circuit be properly con- 
nected to the brushes, a current will flow through the field 
magnets due to the residual volts; the number of lines of force 
of the field increases with this increase in field strength; the 
induced volts also increase and cause additional current to flow 
around the fields, resulting in a further increase of voltage at 
the brushes. This action continues until the maximum volt- 
age of the machine is attained. The process has been termed 
" the building up of the field," and may be observed by the 
increasing deflection of a voltmeter, or by the gradual increase 
in the brilliancy of a lamp, called a pilot lamp, connected to the 
brushes when any direct-current shunt-wound dynamo starts to 
generate. Ten to twenty seconds may be required from the time 
the field switch is closed until the armature generates its full 
voltage. A machine may refuse to build up, owing to the 
loss of its residual magnetism, in which case the cores should 
be remagnetized. 

Problem 120. — The resistance of the armature of a dynamo is 0.15 
ohm and that of the field magnets, 100 ohms. With open fields the arma- 
ture generates 6 volts, due to the residual magnetism. What current 
will flow around the field to start the building-up process when the field 
circuit is closed? 

By Formula (35) I = -^ = ^ = 0.059 ampere. 



DIRECT-CURRENT GENERATORS 



421 



300. The Shunt Generator — Constant Potential. — In a 
shunt dynamo (Fig. 363) the field coils are of comparatively 
high resistance as compared with the armature; for example, 
the multipolar field of a 125-volt, 10-kw. dynamo has a resis- 
tance of about 40 ohms, and the armature resistance is only 
0.1 ohm. The field ampere-turns of a shunt generator are the 
product of a very small 
current and a great many 
turns, so that httle of the 
electric energy generated 
will be used for their excita- 
tion. The regulation of the 
voltage in the external cir- 
cuit of a shunt machine is 
accomphshed by varying 
the current through the 
field coils, by means of a 
resistance inserted in series 
with them, and called the 
field rheostat (Fig. 363) . De- 
creasing the resistance in 
the field rheostat increases 
the current around the field 
coils, thereby increasing the ampere-turns, the number of lines 
of force cut by the armature, and the induced voltage in the 
armature winding. Inserting resistance in the field rheostat 
lowers the voltage available at the brushes. 

The current flowing through the shunt field is equal to the 
potential difference at the brushes, divided by the resistance of the 
field plus that in the field rheostat (Formula 27). 

The current fiowing through the armature of a shunt generator 
is the sum of the currents in the field circuit and in the external 
circuit. The volts drop in the armature is equal to its resistance 
multiplied by the current flowing through it (Formula 28) . 

-The resistance of the armature is usually measured by the 
voltmeter-ammeter method (Tf 228) and will be higher when 
the machine is carrying a load than when running idle on 
account of the resistance increase occasioned by heating. It is 
usually measured directly after a load test on the machine. 




Fig. 363. — Shunt Generator. 



The field magnets are connected across the 
brushes. A field rheostat regulates the voltage. 



422 LESSONS IN PRACTICAL ELECTRICITY 

301. Action of the Shunt Generator. — In starting a shunt 
generator, after proper speed is attained, the machine is brought 
up to the required voltage by manipulating the field rheostat, 
and then the main switch connecting it with the external 
circuit is closed. Suppose that the voltmeter indicates 112 
volts potential difference when the external circuit is open. 
The induced E. M. F. will be a httle higher than this value 
and equal to 112 + I x r, where I equals the current through 
the fields and r equals the armature resistance. A voltmeter, 
therefore, placed across the brushes of any self -exciting gen- 
erator indicates the potential difference rather than the in- 
duced E. M. F. 

If the field rheostat is adjusted for any particular voltage 
with the main circuit open, say 112 volts, and the switch is 
now closed so that more current flows from the armature, the 
voltmeter at once indicates a lower voltage, say 108 volts. 
If the speed is the same as before, this loss is due to two causes: 
first, there is an increased drop in the armature due to the 
additional current flowing through it, which lowers the po- 
tential difference at the brushes; second, the potential dif- 
ference at the brushes being lowered, less current flows around 
the field, so that there are not quite so many lines of force 
cut as before. 

A statement of the voltages of a generator at no load and 
when carrying full load is spoken of as its voltage regulation. 
The percentage regulation is the ratio of the change in volt- 
age between no load and full load to the voltage at full load. 

To FIND THE PERCENTAGE REGULATION OF A GENERATOR: 

Obtain the difference between the no-load and full-load voltages 
of the machine and divide by the full-load voltage. 

-. , . no-load voltage - full-load voltage .-^s 

% voltage regulation = p-rr-j — -. r- (99). 

full-load voltage 

Problem 121. — The voltage of a shunt generator when operating at 
no load is 112 and when operating at full load is 108. Find its voltage 
regulation. 

112-108 4 

By Formula (99) % regulation = —"^TT^ — " Tns " ^'^^"^ " ^'"^ P^^ ^^^** 



DIRECT-CURRENT GENERATORS 



423 



The potential difference at the brushes thus varies in a 
shunt generator, with each change in load, increasing as the 
load decreases and decreasing as the load increases. If the cur- 
rent fluctuations are wide and quite frequent, an attendant 
would be constantly required to manipulate the field rheostat, 
or else some automatic device may be employed to keep the 
voltage constant. In consequence, shunt generators are 
adapted only to installations where the load is fairly constant, 




Fig. 364. — Two Shunt Generators Connected in Parallel. 

The voltage across the mains is equal to that of one machine, the current 
■ in the mains is equal to the sum of that of the two machines. 

when they will require very little attention after the proper 
adjustment of the field rheostat has been made. 

Shunt generators may be connected in parallel when their 
voltages are equal by connecting the positive and negative 
brushes as in Fig. 364. The voltage is the same as with one 
machine, but the current output will be the sum of the currents 
each machine can furnish separately. The voltage of a ma- 
chine, to be paralleled with other generators already in service, 
should be adjusted equal to, or a little higher than, their po- 
tential, after which adjustment it can be connected to the 
common circuit. Such machines in parallel operation are 
practically self-adjusting to load conditions. If one machine 
runs a little faster than the rest it will do more work, and vice 
versa. Their voltages should be carefully regulated so that 
the total load will be properly apportioned among them. To 



424 



LESSONS IN PRACTICAL ELECTRICITY 



take load off one machine running in parallel with others, add 
resistance gradually in its field circuit, until the ammeter of 
that machine reads practically zero, after which its circuit 
breaker (Fig. 146) is tripped and the main switch opened. 

Shunt generators will also operate in series, but if the ma- 
chines are of different sizes, the current in the external cir- 
cuit is limited to the capacity of the smaller machine. The 
polarity of the brushes of a shunt generator may be changed 
by either reversing the field connections to the brushes, or by 
reversing the direction in which the armature rotates. In 
the latter case the brushes will also have to be changed to agree 
with the direction of rotation. 

Experiment 100. — The following test, No. 1, was made upon a certain 
1-kw. shunt-wound generator and illustrates the falling of potential at 
the brushes as the load increases. The voltmeter was placed across the 
brushes, the ammeter was placed in series with some lamps joined in 
parallel, and the shunt field rheostat was adjusted so that the E. M. F. 
was 110 volts with no load. The rheostat was not adjusted thereafter 
during the test. Readings of the voltmeter and ammeter follow for a con- 
stant speed of 1540 rev. per min. 



Test No. 1. 



Test No. 2. 



Amperes 


Volts at Brushes 


Speed 


Volts at Brushes 


1 


108 


2110 


100 


2 


106 


2200 


104 


3 


103 


2290 


108 


4 


100 


2380 


112 


5 


97 


. 2470 


116 



Experiment 101. — The field magnets of the foregoing generator were 

separately excited so 
,37-0hm5 ^ Leads oodOhm that the lines of force 

cut were the same at 
all speeds. The field 
rheostat was adjusted 
so that the generator 
produced 100 volts at 
a speed of 2110 rev. 
per min. The voltage 

at various speeds is shown above for Test 2 and illustrates how the induced 

volts vary proportionally with the speed. 




Fig. 365. — E.M.F. and P.D. of a Shunt 
Generator. 



DIRECT-CURRENT GENERATORS 



425 



Problem 122. — A shunt generator, Fig. 365, maintains 110 volts 
across 100 incandescent lamps joined in parallel, requiring 55 watts and 110 
volts each. The lamps are located some distance from the generator 
and the resistance of the leads is 0.02 ohm. Resistance of armature is 
0.03 ohm and of field coils is 37 ohms. Find: 

(a) P. D. at brushes; (b) total E. M. F. generated; (c) watts lost 
in the armature; (d) loss in the field; (e) loss in the leads; (f) power 
supplied to the lamps. 

By Formula (55) I 

(28) E 



55 



X 100 = 50 amperes for lamps. 



(27) I 



3 amperes through the fields. 



P ^ 

E ~ 110 

I X R = 50 X 0.02 = 1 volt drop in leads. 

110 + 1 = 111 volts P. D. at brushes (a). 
E 111 
R ~ 37 

50+3 =53 amperes through the armature. 
(28) E=IxR=53x 0.03 = 1.59 volts drop in armature. 

1.59 + 111 = 112.59 volts total E. M. F. (b). 
(54) P=ExI =1.59 X 53 =84.3 watts lost in arma- 
ture (c). 

111 X 3 =333 watts lost in fields (d). 
1 X 50 = 50 watts lost in leads (e). 

110 X 50 = 5500 watts supplied to lamps (f). 

302. Action of the Series Generator (Constant Current). — 
In a series generator (Fig. 366) the field coils are in series with 
the armature, and have a low re- 
sistance, since the current from the 
armature flows through them to the 
external circuit. The field ampere- 
turns of a series generator, as com- 
pared with those of the shunt ma- 
chine, are the product of a much 
larger current and a less number of 
turns. With the armature running 
at a constant speed, the E. M. F. 
and current from a series generator 
will vary with every change in the 
resistance of the external circuit, 
since each change of current alters 
the field magnetizing current, and 
consequently the E. M. F. induced in the armature. In practice 
the current from a series generator is required to be constant, 
irrespective of the resistance of the external circuit, while the 




Fig. 366. — Series Generator. 



426 



LESSONS IN PRACTICAL ELECTRICITY 



voltage is altered to suit the conditions of the circuit. It is thus 
a constant-current generator. The regulation is accomplished by 
either of two general methods. In the first method the arma- 
ture used is of the open coil type (H 288) and the position of 
the brushes is automatically moved so as to be in connection 
with the armature coils while they are passing through any 
stage of induction, from the points of maximum induced 
E. M. F. to the minimum. Any change in the current strength 
tending to change the field magnetism is thus neutralized by 
a corresponding opposite change in the E. M. F. The auto- 
matic regulator is 

Series Field 




Fig. 367. — Regulating the Voltage of a Series 
Generator by Shunting the Series Field. 



usually a solenoid 
and core attached to 
the brushes and 
actuated by the 
main current. This 
method is utilized in 
the Thomson-Hous- 
ton arc-light dynamo. 
In the second 
method an adjust- 
able rheostat is 
placed in shunt with 
the series field mag- 



nets (Fig. 367) and the main current divides in proportion to the 
resistances of the two circuits. The arm of the rheostat is auto- 
matically moved by a solenoid and core arrangement actuated 
by the main current. If the resistance of the external circuit is 
suddenly lowered, the increased current immediately actuates 
the solenoid and rheostat arm in a direction to decrease its 
resistance, thereby shunting more current from the field circuit, 
and preventing the rise of E. M. F. This second method is used 
in the Brush arc-light generator. Obviously a series generator 
will not self -excite when the external circuit is open, and will not 
'' build up " when the external resistance is very high. This may 
be overcome by momentarily short-circuiting the machine while 
the external circuit is closed, when the E. M. F. will rise to a 
sufficient value to start the action. With a sensitive automatic 
regulator a series machine may be short-circuited without 



DIRECT-CURRENT GENERATORS 



427 



injury, since the larger current which would tend to flow, 
immediately actuates the automatic mechanism in such a 
manner as to decrease the E. M. F. 

Series generators were formerly used as constant-current 
generators for the operation of arc lamps connected in series, 
but few of them are now in service. The series field winding 
is still retained however in the compound-wound generator, 
^ 303. 

303. Compound Machines {Constant Potential). — The 
compound-wound generator is designed to automatically give 
a better regulation of voltage on constant-potential circuits 
than is possible with 
a shunt machine, and 
possesses the char- 
acteristics of both the 
series and shunt dy- 
namos. The shunt 
field is the same as 
in the shunt genera- 
tor, and independent 
series field spools are 
added, through which 
the main current 
flows. These are 
connected so as to increase the magnetism of each pole produced 
by the shunt winding (Fig. 368). With no current in the exter- 
nal circuit the machine separately excites by its shunt field. 
When current flows to the external circuit the voltage at the 
brushes is not lowered, as in the shunt generator, since the 
series winding strengthens the field by the current flowing 
through it, and thus raises the voltage in proportion to the in- 
creased current. By a proper selection of the number of turns 
in the series coils, the voltage is thus kept automatically constant 
for wide fluctuations in load without changing the shunt field 
rheostat. If a greater number of turns is used in the series coil 
than required for constant terminal voltage at all loads, the volt- 
age will rise as the load is increased, and thus make up for the 
loss on the transmission lines, so that a constant voltage will 
then be maintained at some point distant from the generator. 




Fig. 368. — Compound-wound Generator, 

The series and shunt fields act in unison. 



428 LESSONS IN PRACTICAL ELECTRICITY 

The machine is then said to be over-compounded. In Ughting 
generators this over- compounding is usually designed for a rise of 
voltage from 3 to 5 per cent of that of the machine, from no load 
to full load. In design, the series field coils are wound with a 
slightly greater number of turns than actually required, and the 
amount of compound is determined by a load test after com- 
pletion. These adjustments are made by placing a shunt around 
the series field so that the main current divides between the two 
circuits. The length of the shunt can then be regulated to send 
sufficient current around the series coils to produce the desired 

" 




Fig. 369. — Ridgway Generator and Engine. 

compounding. In a short-shunt compound-wound generator 
the shunt field is subjected to a higher voltage than with the long- 
shunt connections. The E. M. F. applied to the shunt field in 
the latter case for any particular load is equal to the E. M. F. 
at the brushes minus the drop on the series field (see Figs. 
358 and 359). Compound-wound direct-current generators 
are extensively used in electric lighting and power stations 
and in electric railway power stations where the load is very 
fluctuating. A compound-wound generator direct connected 
to a steam engine is shown in Fig. 369. 

A short-circuit on a compound-wound generator overloads 
the machine, since the excessive current flowing through the 
series field tends to keep the voltage at its normal value. Un- 
less the line is automatically opened under such a condition, 



DIRECT-CURRENT GENERATORS 



429 



either by a fuse or automatic circuit breaker, the machine and 
its driving engine will be damaged. 

Experiment 102. — The following test was made on the 1-kw. generator 
referred to in Experiment 100. The series field was short-circuited in the 
previous tests, but both fields are acting in the present one. The ma- 
chine was adjusted to 110 volts by the shunt field rheostat as before, 
and not changed during the test. It will be noted that the potential 
was constant whether 1 ampere or 5 amperes were drawn from the machine. 
Compare with the shunt generator test in ^ 301. 



.40 Ohms 



Series 0.020hm. 




Leads 0.02 Ohm 






112 
Volfs 



100 Amperes 




Fig. 370. 



— ISFeef J 

E.M.F. and Losses of a Compound-wound Generator. 



Compound-wound Generator Test. 



Amperes. 


Speed. 


Volts at 
Brushes. 


1 
2 
3 
4 
5 


1540 
1540 
1540 
1540 
1540 


no 
no 
no 
no 
no 



Problem 123. A compound-wound generator (Fig. 370) supplies 100 
amperes at 112 volts to a group of lamps located 75 feet from the gen- 
erator. Resistances are: leads 0.02 ohm; armature 0.01 ohm; series coil 
0.02 ohm; shunt coil 40 ohms. Find: 

(a) P. D. at brushes; (b) total E. M. F. generated; (c) watts lost 
in the leads; (d) loss in the series coil; (e) loss in the shunt coil; (f) 
loss in the armature; (g) power supplied to the external circuit. 

By Formula (28) E = IxR=100x0.02=2 volts drop in leads. 
112 + 2 = 114 volts P. D. at terminals. 
(28) E = I X R = 100 X 0.02 = 2 volts drop on series 
field. 
114 + 2 = 116 volts P. D. at brushes (a). 



(27)1=^ 



E 116 



40 



= 2.9 amperes through shunt field. 



430 LESSONS IN PRACTICAL ELECTRICITY 

100 + 2.9 = 102.9 amperes, total current through 
armature. 
(28) E = I X R = 102.9 x 0.01 = 1.029 volts drop in 
armature. 
E. M. F. =112 volts (lamps) + 2 volts (leads) + 2 
volts (series coil) + 1 . 029 volts (armature) = 
117.03 volts (b). 
(60) P = P X R = 100 X 100 X 0. 02 = 200 watts (c) ; 
= 100 X 100 X 0.02 = 200 watts (d); 
= 2. 9 X 2. 9 X 40 = 336. 4 watts (e); 
= 102. 9 X 102. 9 X 0. 01 = 105. 88 watts (f). 
(54) P = E X I = 114 X 100 = 11400 watts supplied to 
external circuit (g). 

304. Compound-wound Generators in ParalleL ^- Com- 
pound-wound generators are generally run in parallel, but 
more care must be exercised in connecting them in circuit than 
with shunt machines. In order to connect several compound- 
wound generators in parallel a special connection between the 
machines, called an equalizing bar, must be used. The function 
of this equalizer is to enable each machine to take its share 
of the load and to make the load on the machines so paralleled, 
independent of slight changes in speed. The equalizing bar 
(Fig. 371) connects the brush of one generator, to which the 
series field is attached, to the corresponding brush of another 
generator. Both brushes, so connected, are of the same 
polarity and also of the same potential when the machines 
run at the same voltage. 

The action is as follows: suppose the compound-wound 
generator No. 1 (Fig. 371) is carrying a load and it is desired 
to parallel machine No. 2 with it; the latter is brought up to 
speed and its voltage regulated by the shunt field rheostat F2 
until a voltmeter indicates that it is equal to that of No. 1. 
Though the terminals of the loaded and free machines now 
have the same potential difference, the voltage at the brushes 
of the loaded machine will be higher than that of the other, 
by an amount equal to the drop on the series field of No. 1. 
There is thus a difference of potential between the two ends 
of the equalizing bar, and when its switch E is closed, some 
current flows through the equalizer and around the series field 
of machine No. 2 to the external circuit. The line switch S2 
is now closed and the free machine takes some portion of the 



DIRECT-CURRENT GENERATORS 



431 



load and is further regulated by its shunt field rheostat. When 
complete equalization of load occurs there will be no current in 
the equalizer. If the speed of either machine falls, thereby 
lowering its voltage, current from the other machine will flow 
through the equalizer and strengthen its series field, thus in- 
creasing the voltage. Sometimes no current will flow in an 
equalizer while at other times it may flow in either one direction 
or the other. To reduce the I^R loss, the equalizer should be 
as short as possible and as large as the main generator cables. 
A triple-pole switch is generally used for coupling a com- 
pound generator with others, the middle blade of which is 




Fig. 371. — Two Compound-wound Generators Connected in Parallel. 



slightly longer than the other two, and is connected to the 
equalizer. When the switch is closed the equalizer is con- 
nected first and the main terminals a little later. In shutting 
down a generator in parallel with others the main line terminals 
are first disconnected and then the equalizer is opened; this 
action is performed in one operation with the triple-pole switch 
alluded to above. The voltage should then be lowered by in- 
serting all the resistance of the shunt field rheostat in circuit, 
after which this field circuit may be opened, and then the speed 
reduced. 

Any number of compound-wound generators may be oper- 
ated in parallel. If the machines are of different capacities 
they may also be run in parallel, provided that their voltages 
are the same, and that the resistances of the series fields are 
inversely proportional to the current capacities of the several 



432 



LESSONS IN PRACTICAL ELECTRICITY 



machines to be connected. Each machine will then take load 
in proportion to its capacity. The series fields can be adjusted 
by adding several turns of extra wire to this circuit, as required. 
305. Three-Wire Generators. — In the three-wire system 
of electrical distribution to be described later (H 336) it is 
usual to have about 115 volts P. D. between each outside 
wire and the central or neutral wire, and twice that voltage 
between the two outside wires. Obviously two 115-volt 
generators might be connected in series and the neutral wire 




U 



iii 



Fig. 372. — Three-wire Generator Having Reactance Coil 
Mounted on Armature. 

joined to the connection between the machines (see Fig. 399), 
but this arrangement involves the expense for two machines. 
Therefore machines have been designed to meet this condition 
so that only one generator, called a three-wire generator, is 
necessary to supply a three-wire distribution circuit. 

In one type of three-wire generator, originally designed by 
Dobrowolsky, a low-resistance coil of wire wound on an iron 
core is mounted on the armature and connected as shown in 
Fig. 372. In a bipolar machine this coil is connected to the 
regular armature winding at points a and b which are dia- 
metrically opposite, and the neutral wire is joined to the mid- 
point c of the coil by means of a slip ring and brush. The 
E. M. F. across the terminals a and b is alternating, and conse- 



DIRECT-CURRENT GENERATORS 



433 



quently an alternating current will flow through the coil, but 

its value is small because of the large inductance of the coil. 

The midpoint c will 

then have a potential 

midway between the 

potentials of the 

brushes connected to 

the outside wires. If - 

the load taken from 

one side of the circuit 

is the same as that 

from the other, no 

direct current will 

flow through the coil ^^S* '^^^- — Armature of Three-wire Generator. 

nor in the neutral Midpoint of revolving coil connects with the slip ring, 

wire. But if the loads are unbalanced the neutral wire and the 
coil will carry a direct current whose strength depends upon the 
amount of unbalance. Fig. 373 shows the armature of a three- 





Fig. 374. — Three-wire Generator with Auxiliary Winding. 

wire generator made by the Burke Electric Co. The coil in this 

machine is wound in the same slots with the armature winding. 

Another type of three-wire generator produces the voltage 

for the neutral wire by a separate winding ab as depicted in 



434 LESSONS IN PRACTICAL ELECTRICITY 

Fig. 374. This winding contains just half the number of 
turns between the sUp ring and the point a, where it connects 
with the main winding, that there are in the latter winding 
between brushes, and in consequence the auxiliary winding 
will generate one-half the voltage that exists between the 
brushes. The Crocker-Wheeler Co. manufactures generators 
on this principle, but employs several auxiUary windings 
properly connected and distributed in the regular slots over 
the armature face. 

In compounded three-wire generators the series field coils 
are divided into two equal sections, one section being con- 
nected in series with one of the outer wires and the other 
section in series with the other outer wire. 

306. Capacity of a Generator. — The capacity or rating of 
a generator depends very largely upon its heating when in 
service, and also upon commutating conditions. Eddy-cur- 
rent and hysteresis loss in the core, together with copper loss 
in the armature and field windings, produce heat in the gen- 
erator, and its temperature continues to rise until the heat is 
dissipated as fast as it is produced. Since the copper loss 
increases very rapidly with load (heat increases four-fold when 
the current is doubled (H 237) a limit is soon reached beyond 
which the machine could not be run without speedy deteriora- 
tion. This limit is imposed chiefly by the insulation employed. 
The American Institute of Electrical Engineers in its 1918 
Standardization Rules gives the limits for hottest-spot tempera- 
tures of insulations as foUows: 

A. — Cotton, silk, paper and similar materials, when so 
treated or impregnated as to increase the thermal limit,^ also 
enameled wire — 105° C. or 221° F. 

B. — Mica, asbestos and other materials capable of resisting 
high temperatures, in which only Class A material or binder 
is used for structural purposes only — 125° C. or 257° F. 

If this maximum temperature be exceeded, the insulation 
may be endangered, and in addition the excess load may lead 
to injury by exceeding Umits other than those of temperature, 
such as commutation, stalhng load and mechanical strength. 

1 When not treated or impregnated, the limit is 10° C. or 18° F. less 
than above mentioned. 



DIRECT-CURRENT GENERATORS 435 

In determining the temperature of different parts of a ma- 
chine a thermometer is apphed to the hottest accessible part 
of the completed machine and the hottest-spot temperature 
for the winding is obtained by adding a correction of 15° C. 
(27° F.) to the highest temperature observed, in order to 
allow for the practical impossibility of locating the thermometer 
at the hottest spot. When the thermometer is applied directly 
to the surfaces of bare windings, such as an edgewise-wound 
strip conductor or a cast copper winding, a correction of 5° C, 
instead of 15° C. is made. For commutators, for collector 
rings, or for bare metalHc surfaces not forming part of a wind- 
ing, no correction is apphed. Thermometers used for taking 
temperatures of machines should be covered by felt pads 
IJ inches x 2 inches x i inch, cemented or puttied on. Meas- 
urements of temperature of windings may also be made by 
means of their increase in resistance or by the use of embedded 
temperature detectors such as thermal couples. 

In order to determine the continuous rating of a machine 
it is operated under load conditions until a constant tempera- 
ture difference between the machine and the surrounding air 
is reached. Under full load this may require from 6 to 20 
hours, according to the size and construction of the machine. 
In such a test on a generator conducted in an engine room 
whose temperature is 100° F. the permissible rise of temperature 
as observed by thermometer would be 221 - 27 - 100 = 94° F. 
for impregnated cotton-insulated windings and would be 221 — 
100 = 121° F. for the commutator. 

307. Commercial Rating of Generators. — Direct-current 
generators are rated in size, according to the number of kilo- 
watts which they are capable of maintaining in the circuit ex- 
ternal to their terminals within the hmit of permissible heating. 
For example, a 50-kw., 100- volt generator means that the ma- 
chine will deliver without excessive heating 50 kw. to the 
circuit external to its terminals,^ and that 100 volts P. D. 
will be maintained at this output across the terminals. The 

' ^The potential difference at the brushes and the terminals of shunt 
generators is practically the same, but in a series or compound-wound 
generator the potential at the brushes is higher than that at the terminals, 
on account of the I R drop in the series field, ^1[ 300 and 303. 



436 LESSONS IN PRACTICAL ELECTRICITY 

current, therefore, at full load will be, by Formula (55) 50,000 
-^ 100 = 500 amperes. 

Owing to the electrical losses in the armature and fields the 
total kilowatts generated is higher than the machine's rating. 
For example, the 50-kw. machine alluded to may develop 
55 kw., of which only 50 kw. can be utilized in the external 
circuit. 

308. Losses in a Dynamo. — There are two classes of 
losses in a dynamo, 

(1) Mechanical losses, 

(2) Electrical losses. 

(1) The mechanical losses include the friction between 
the rotating armature shaft and its bearings, windage, and 
the friction of the brushes upon the commutator. These 
friction losses are practically the same at all loads, and consume 
a certain percentage of the power supplied to the machine, 
which does not therefore appear as useful energy in the ex- 
ternal circuit. 

(2) The electrical losses include the I-R losses in the arma- 
ture and fields and at the brush contacts, the losses due to eddy 
currents (II 289) and hysteresis (H 293). 

Losses in the field rheostat shall be included in the generator 
losses where there is a field rheostat in series with the field 
magnets of the generator, even in separately-excited machines. 
All the losses may be summed up then as due to 

(a) Mechanical friction, 

(b) Electrical friction (resistance), 

(c) Magnetic friction (hysteresis). 

309. Efficiency of a Generator. — The meaning of the term 
efficiency is given in H 151. When the efficiency of a machine 
is stated without specific reference to load conditions, full or 
rated load is always to be understood. The efficiency of a 
generator is the ratio of the energy delivered by it to the energy 
supplied to it, or, 

. output output . 

efficiency = — = — r — — — ; • • • (100). 

input output + losses 



DIRECT-CURRENT GENERATORS 437 

The efficiency therefore considers the mechanical, electrical, 
and magnetic losses given in ^ 308. Its value varies with the 
size of the machine and the load it is supplying. For example, 
a 5-kw. dynamo may have as low an efficiency as 80 per cent; 
a well-designed 40-kw. machine, 90 per cent, and a 500-kw. 
generator, 94 per cent. Again a certain 200-kw. generator has 
an efficiency at full load of 93 per cent, at f load of 92 per 
cent, at J load of 90 per cent, and at i load of 84 per cent. 

To OBTAIN THE EFFICIENCY OF A GENERATOR: 

Divide the energy delivered hy the generator hy the output plus 

the sum of the mechanical, electrical, and magnetic losses. 

Let P = output of generator in watts, 

p = total losses of generator in watts. 

Then the efficiency is (compare Formula 67) 

p 

efficiency = (101). 

P + p 

Problem 124. — It requires 44 kw. (58 H. P.) to drive a 40-kw. gen- 
erator. What is its efficiency? 

Here P = 40 kw. and the input is P + p =44 kw., whence by Formula (101) 

P 40 

efficiency = = — = 0. 91 =91 per cent. 

Problem 125. — Determine the efficiency of the generater considered in 
Problem 123, if 14 kw. are required to drive the machine. 

Input = 14,000 watts; output = 114 x 100 = 11,400 watts, 

therefore efficiency = — '- = 0.81= 81%. 

^ 14,000 

In the case of machinery two efficiencies are recognized, 
conventional efficiency and directly -measured efficiency. Unless 
otherwise specified, the conventional efficiencj^ is to be em- 
ployed. Conventional efficiency of machinery is the ratio of 
the output to the sum of the output and the losses; or of the 
input minus the losses to the input; when, in either case, con- 
ventional values are assigned to one or more of these looses. 
The need for assigning conventional values to certain losses, 
arises from the fact that some of the losses in electrical ma- 
chinery are practicably indeterminable, and must, in many 



438 LESSONS IN PRACTICAL ELECTRICITY 

cases, either be approximated by an approved method of test, 
or else values recommended by the American Institute of Elec- 
trical Engineers and designated " conventional" values shall 
be employed for them in arriving at the conventional efficiency. 
To obtain the directly-measured efficiency, input and output 
determinations may be made directly, measuring the output 
by brake, or equivalent, where applicable. Within the limits 
of practical application, the circulation-power method, some- 
times known as " loading-back " method (^315), may be used. 



QUESTIONS 

1. What is a shunt-wound generator, a series- wound generator, and 
a compound-wound generator? 

2. Since the field magnets of a self-exciting generator are not sup- 
plied with current from any external source, how is it possible for the 
machine to generate? 

3. A 110-volt incandescent lamp is connected to the terminals of a 
series machine running at its proper speed and capable of generating 
4000 volts, yet the lamp fails to light. Why is this? 

4. The main switch of a shunt generator is closed and then the ma- 
chine started up, but it refuses to " build up." Why? 

5. A large number of lamps are suddenly switched off from a circuit 
connected to a shunt generator. What two actions will immediately 
occur at the generator and how will you counteract them? 

6. What are " residual volts " ? 

7. Give two reasons for the fall of potential at the brushes of a shunt 
generator when the current from it is increased. 

8. What is the advantage of a compound-wound generator over a 
shunt machine? 

9. What is the difference in the method of regulating the field mag- 
netizing force of a series and of a shunt machine? 

10. A generator is compounded for 10 per cent of its rated voltage. 
What is meant by this and how is it accomplished? 

11. What is meant by an over-compounded generator? 

12. Since an alternating current, is not suitable for magnetizing field 
magnets, how can an alternator be self -exciting? 

13. What is an exciter, and for what is it used? 

14. What will be the effect of joining two shunt generators in series 
if one machine is rated at 50 kw. and the other- at 100 kw.? Both ma- 
chines have the same E. M. F. 

15. What is an equalizing bar, and for what purpose is it used? 

16. How would you proceed to parallel a compound-wound direct- 
current generator, which is " shut down," with two others that are carry- 
ing loads? 



DIRECT-CURRENT GENERATORS 439 

17. How would you disconnect and shut down one of the machines 
in Question 16? 

18. Make diagrammatic sketches of all the different methods of field 
excitation with which you are familiar. 

19. How may a shunt generator be designed to supply current to 
both sides of a three-wire distribution circuit? 

20. Explain what determines the capacity of a dynamo. 

21. What is meant by the efficiency of a generator? 



PROBLEMS 

1. The E. M, F. of a shunt- wound railway generator rises from 500 
volts at full load to 590 volts upon disconnecting the load. What is the 
regulation of the machine in per cent? Ans. 18%. 

2. A series dynamo has an armature resistance of 0.03 ohm and a field 
resistance of 0.01 ohm; the machine is connected to lamps requiring 14 
amperes and having a resistance of 4 ohms; the resistance of the lead 
wires is 0.4 ohm. The generator requires 1| H. P. to drive it. Find 
the following: (a) total E. M. F. generated, (6) P. D. at the brushes, 
(c) efficiency. Ans. (a) 62.16 volts; (5) 61.74 volts; (c) 77%. 

.3. A shunt dynamo is driven as a generator to supply 150 lamps, con- 
nected in parallel, each having a resistance of 60 ohms (hot), and re- 
quiring 0.85 ampere. The resistance of the armature is 0.02 ohm, of field 
magnets, 22 ohms; resistance of leads neglected, (a) Find the E. M. F. 
(b) What is the P." D.? Ans. (a) 53.596 volts; (6) 51 volts. 

4. A compound-wound short-shunt generator is connected to 700 in- 
candescent lamps in parallel, each having a resistance of 220 ohms (hot) 
and requiring 110 volts. Resistance of leads, 0.02 ohms, shunt field, 40 
ohms, series field, 0.015 ohm, armatm-e, 0.025 ohm. It requires 70 H. P. 
to drive' the machine. Find the following: (a) E. M. F. generated, 
(6) P. D. at brushes, (c) drop on series field, (d) watts lost in shunt 
field, (e) watts lost on the line, (/) efficiency. Ans. (a) 131.076 volts; (b) 
122.25 volts; (c) 5.25 volts; (d) 373.5 watts; (e) 2450 watts; (/) 78%. 

5. The efficiency of a 175-kw. generator is 87.5 per cent. How much 
energy is supplied to the machine? Ans. 200 kw. 



LESSON XXVI 



DIRECT-CURRENT MOTORS 



Comparison Between a Generator and a Motor — Direction of Rotation 
of Series and Shunt Motors — Position of the Brushes on a Motor — 
Counter Electromotive Force of a Motor — Current Taken by a 
Motor — Mechanical Power of a Motor — Torque — Output and 
Efficiency of Motors — Starting Motors — Speed Control of the 
Shunt Motor — Speed Regulation — Characteristic Curves of Motors 
— Electric Traction — Direct-Current Motor- Generator Sets — Ques- 
tions and Problems. 

310. Comparison Between a Generator and a Motor. — A 

generator is a machine for generating electrical energy by mov- 
ing conductors in a magnetic field, the force necessary to 
maintain the motion being supplied by a steam engine or 




Fig. 375. — Multipolar Direct-current Motor. 

other source of power. An electric motor is just the reverse 
of a generator, and is a machine for converting electrical power 
supplied to it into mechanical power at the motor pulley. 
When the field magnets of a dynamo, as Fig. 375, are excited 
and a current is passed through its armature by means of the 

440 



DIRECT-CURRENT MOTORS 



441 I 



brushes, the armature will revolve in the magnetic field. The 
rotation is due to the interaction between the magnetic field 
of the current-carrying wires upon the armature, and that pro- 
duced by the field magnets. An electric motor, for direct cur- 
rents, is constructed in the same manner as a generator. Any 




Fig. 376. — Dissected View of Type RC Shunt Motor. 

machine that can be used as a generator will, when supplied 
with electrical power, run as an electric motor, and conversely, 
a motor, when driven by mechanical power, will supply electrical 
energy to the circuit connected to it. In fact, the terms gen- 
erator a,nd motor are applied to a dynamo to indicate the 
direction of energy conversion, whether from mechanical to 
electrical, or vice versa. 



442 LESSONS IN PRACTICAL ELECTRICITY 

The previous lessons on the construction of generators will 
apply equally well to electric motors, although there are some 
differences in appearance imposed by the location of the 
machines. Motors are classified in the same manner as genera- 
tors, and may be (a) series wound, (b) shunt wound, and (c) 
compound wound. 

The general appearance of a direct-current motor is seen 
from Fig. 375, which shows a 20-H. P. motor made by the Gen- 
eral Electric Co. A dissected view of this machine appears in 
Fig. 376, wherein the principal parts can be more clearly seen. 

List of Principal Motor Parts, Fig. 376. 

A — Shield at commutator-end of machine. 

B — Frame of 4-pole motor showing three main (large) poles 
and two commutating poles in place. One pole of each 
kind is illustrated without its coil. 

C — Shield at pulley-end of machine. 

D — Main (shunt) field coil of insulated wire wound on horn- 
fiber spool. 

E — Commutating field coil. 

F — Brush-holder yoke, brushes and brush holders. 

G — Armature core of laminated steel disks clamped together 
and keyed to shaft; recessing is for binding wire which 
keeps armature wires in slots. 

H — Commutator built up of many copper segments separated 
by mica strips. 

311. Direction of Rotation of Series and Shunt Motors. — If 

the polarity of the field magnets and the direction of current 
flow through the armature of a motor are known, the direction 
of rotation of the armature can be determined by the left-hand 
rule, page 218 (see also Fig. 323). 

A series dynamo when supplied with current becomes a series 
motor, Fig. 366, and will run in the opposite direction to its 
motion as a generator. Reversing the direction of current at 
its terminals will not change the direction of rotation, since the 
current will still flow through the armature in the same direction 
as through the field. It is necessary to reverse either the arma- 
ture or field connections to change the direction of motion. 



DIRECT-CURRENT MOTORS 443 

A shunt dynamo runs in the same direction when used as a 
shunt motor as when used as a generator. This will be seen 
from Fig. 363; if a current from an external source enters 
by the lower brush it will flow up through the armature in the 
same direction as when it is used as a generator, but the current 
through the fields will be reversed from the direction indicated 
in the figure, since the fields are in parallel with the brushes. 

Experiment 103. — Connect and operate the student's experimental 
dynamo, Fig. 312, as a shunt motor. Reverse the current at the motor 
terminals and the direction of rotation will be found the same as before. 
Why? Now reverse the direction of rotation, H 189. 

Experiment 104. — Connect the armature of the motor used in Experi- 
ment 103 in series wdth the two field coils in parallel, so that the poles have 
the proper polarity, N and S. It is now a series motor, (a) Apply the 
left-hand rule, page 218, for the direction of rotation of the armature, 
(b) Reverse the direction of rotation. 

312. Position of the Brushes on a Motor. — The reaction 
of the armature current upon the field of a motor distorts that 
field just as in a generator. If 294, except that the lines of force 
are now crowded together in the leading pole tips and lessened 
in the trailing tips, so that the flux distribution is just opposite 
to that illustrated in Fig. 346. The commutation plane will, 
therefore, advance backward against the direction of rotation 
of the motor, and it is at this position that commutation in a 
motor should take place. The brushes are set in the same 
manner as given for a generator in ^ 295, but are rocked hack- 
ward against the direction of rotation until the non-sparking posi- 
tion is found. The angle of advance against the direction of 
rotation will increase as the current taken by the motor in- 
creases, or as the work it is required to perform increases, and 
decrease as the load is removed. In motors with interpoles or 
compensated windings (*[ 296) the brushes may be retained in 
the same position with variations in load. The conditions and 
remedies for the sparking at the brushes of a motor are the 
same as those given in ^ 297. 

313. Counter Electromotive Force of a Motor. — The wires 
of a motor armature, rotating in its own magnetic field, cut 
the lines of force just as if it were being driven as a generator, 
and consequently there is an induced E. M. F. in them. By 



444 



LESSONS IN PRACTICAL ELECTRICITY 



Rotation 



applying the right- and left-hand rules to the single coil in 
Fig. 377, it will be seen that if it is rotated counter clockwise 
by a prime mover, the directio-n of the induced E. M. F. will 
tend to send a current around the coil from D to C, to B, to A, 
while when supplied with current as a motor, to rotate in the 
same direction, the applied voltage will oppose the induced 
pressure and cause a current to flow from A to B, to C, to D. 
This induced pressure in a motor is called its counter electromo- 
tive force (sometimes abbreviated C. E. M. F.) and is always 

in such a direction as to op- 
pose the pressure applied to 
the motor terminals, or to 
that of the supply mains. 
The dotted arrows, in Fig. 
377, indicate the direction of 
the counter E. M. F., and the 
solid arrows, that of the ap- 
phed E. M. F. as found by 
the right- and left-hand rules. 
A motor, without load, will 
run at such speed that its 
counter E. M. F. will very 
nearly equal the applied pres- 
sure. 

The counter E. M. F. of a motor running at any speed 
will be the same as when it is run as a generator at this speed, 
provided the field strength is the same in both cases, hence to 
find the counter E. M. F. of a motor at any speed, run it as a 
generator at this speed and measure the induced E. M. F. by 
a voltmeter. The presence of a counter E. M. F. may also be 
observed by connecting a lamp across the terminals of a shunt 
motor, running without much load, and opening the riiain 
supply circuit. The lamp will remain illuminated and gradually 
become dim as the speed of the motor decreases. A voltmeter 
connected across the motor terminals will also indicate, by the 
direction of deflection of the pointer, that the counter E. M. F. 
is opposed to that of the line E. M. F. when the supply switch 
is opened. 

The counter E. M. F. in a motor can never equal the applied 



N 


U 


>/—D S 




/ ) 




W 


\ 


To Supply Circuit 



Fig. 377. — Single-coil Armature 
of Bipolar Motor. 

Full arrows show applied E.M.F., while dotted 
arrows show direction of counter E.M.F. 



DIRECT-CURRENT MOTORS 445 

E. M. F., but is always less by an amount equal to the drop 
in the motor armature, (I x r). The difference between a 
dynamo operating as a generator and as a motor is as follows: 

Motor 
The armature is supplied with 
current from an outside source and 
the interaction of the fluxes from 
armature and field causes rotation 
of the armature. 

This rotation occasions a counter 
E. M. F. in the armature which op- 
poses the current supphed. The 
work done by the outside source in 
overcoming this C. E. M. F. is the 
work which appears as mechanical 
energy at the motor pulley. 



Generator 

The armature is driven by out- 
side mechanical power in a magnetic 
field and an E. M. F. is induced in it 
which sets up a current in the ex- 
ternal circuit. 

This current occasions an elec- 
trodynamic force which opposes the 
motion of armature. The work 
done by the prime mover in over- 
coming this opposition is the work 
which maintains the current in the 
generator circuit. 



To FIND THE CURRENT FLOWING THROUGH THE ARMATURE 
OF A MOTOR : 

Subtract the counter E. M. F. from the applied E. M. F. and 
divide this result by the armature resistance. Ohm's Law for a 
motor is as follows: 
Let 

E = E. M. F. applied at motor brushes, 
& = counter E. M. F. developed by motor, 
I = current through motor armature, 
r = internal resistance of motor armature. 



Then 



1 = ^^ (102). 



The speed which any motor attains is such that the sum of the 
counter E. M. F. developed and the drop in the armature is 
exactly equal to the applied E. M. F. This is expressed by the 
following formula derived by transposition from Formula 
(102): 

Counter E. M. F. + (I x r) = applied E. M. F., 
or ^ 4- (I X r) = E (103). 

The voltage drop in the armature of a motor is a small per- 
centage of the applied pressure, perhaps about 2 per cent of the 
terminal pressure in a 500-kw. motor and about 5 per cent in a 



446 LESSONS IN PRACTICAL ELECTRICITY 

1-kw. motor, so that the counter E. M. F. is not much different 
from the apphed E. M. F. Since the power driving a motor 
equals the apphed pressure times the current, most of which is 
usefully expended in mechanical output, the counter E. M. F. 
is an essential and valuable feature of the motor, rather than 
a detriment to its operation. 

To FIND THE COUNTER E. M. F. OF A MOTOR! 

Multiply the resistance of the armature hy the current flowing 
through it and subtract this product from the E. M. F. applied to 
the motor brushes. The Formula is derived by transposition 
of Formula (103) : 

g = E - (I X r) (104). 

The counter E. M. F. of a motor depends upon the same 
factors as those governing the induced E. M. F. in a generator, 
and is directly proportional to : 

(a) the number of lines of force cut, 

(b) the number of conductors upon the armature, 

(c) the speed at which the lines of force are cut. 

Problem 126. — A small motor is connected to a 110-volt circuit; the 
counter E. M. F. at a particular speed is 100 volts; the resistance of 
the armature is 2 ohms. What current is being supplied to the motor? 

By Formula (102) I = = = 5 amperes. 

r jli 

Problem 127. — The armature resistance of a shunt-wound motor is 0.5 
ohm, and at a certain load 10 amperes flow through it; the voltage at 
the motor brushes is 110 volts. What is the counter E. M. F.? 

By Formula (104) g = E - (Ix r) = 110 - (10 x 0.5) = 105 volts. 

Problem 128. — What current would the motor referred to in Problem 

126 receive if it had no counter E. M. F.? 

F 110 
By Formula (27) I = — = -— = 55 amperes, 
xi 2 • 

314. Current Taken by a Motor. — The current taken by a 
motor depends upon the mechanical load that it carries; the 
larger the load, the greater the current.. This accommodation 
of current to load results in economical operation, and depends 
upon counter electromotive force. There is no counter E. M. F. 
induced in a motor armature until it begins to revolve, so that 
the current flowing through it, when stationary, is equal to 



DIRECT-CURRENT MOTORS 



447 



E -^ R, as in Problem 128. When the armature begins to 
rotate, the current through it gradually diminishes, since the 
counter E. M. F. rises with the speed. It requires more energy 
to start a motor than to maintain it at any particular speed, 
^ 135, so that the counter E. M. F. automatically acts like 
resistance in a circuit, and decrea es the current as the speed 
increases. 

If the load upon a motor be increased the force that it was 
developing is no longer sufficient to overcome the new load 
and consequently its speed falls. The reduction of speed 
lessens the counter E. M. F. and thus permits a greater current 
to flow through the armature, which greater current produces a 
greater force. The automatic adjustment of the current to the 
load is shown in the following experiment: 

Experiment 105. — An ammeter is connected in series with the armature 
of a small motor and the current was noted for several speeds, which were 
read from a speed indicator or tachometer, as follows : 

Motor Test. 



Speed — Revolutions 
per minute 


Amperes 


Speed — Revolutions 
per minute 


Amperes 




500 

1000 


20.0 

16.2 

• 12.2 


1600 
1800 
1950 


7.8 
6.1 
5.1 



At the maximum speed the motor in the above test receives 5.1 
amperes, or about one-fourth of the current which would flow through 
it at rest. If some machinery be now connected to the motor pulley 
by a belt, the motor will slow down somewhat, thus decreasing the 
counter E. M. F. and permitting more current to flow through the 
armature to perform the extra work.' When the load is removed 
the motor increases in speed, thus increasing the counter ^. M. F. 
and decreasing the current taken from the line. There is thus a 
continual automatic adjustment between the current supplied to a motor 
and the work it has to perform, or the electrical power taken from the 
supply mains hy a motor is directly proportional to the mechanical power 
it is required to develop at its pulley. The speed of a shunt motor, running 
fuUy loaded, may be only 5 per cent less than the speed the motor attains 
when running idle. 



448 LESSONS IN PRACTICAL ELECTRICITY 

To FIND THE MECHANICAL POWER DEVELOPED BY A MOTOR: 

Multiply the counter E. M. F. by the current through the 
armature. 

P =^ Xl (105). 

The mechanical power developed includes that required 
for mechanical friction losses and the power which is expended 
in eddy currents and hysteresis. See T[337. 

Problem 129. — (a) What power is developed by a small 110-volt 
motor whose armature resistance is 2 ohms and which runs at a speed 
such as to develop a C. E. M. F. of 100 volts? (b) What power is sup- 
plied to the motor? 

By Formula (102) I = "^-^ = ^^^ ~ ^^^ = 5 amperes (Problem 126). 
r 2 

By Formula (105) P = co x I = 100 x 5 = 500 watts (a). 
By Formula (54) P = E x I = 110 x 5 = 550 watts (b). 

315. Mechanical Power of a Motor — Torque. — The me- 
chanical power of a motor depends upon two factors, the speed 
and the torque, and is equal to the product of these factors. 
The term " torque " is applied to the twisting force which is 
produced in the armature when a current is sent through it, 
and represents the effort made to cause rotation. This effort 
is made up of two components; fir&t, the pull, measured in 
pounds, and second, the length of arm at which this pull acts, 
measured in feet. Thus, a pull of 50 pounds acting at a dis- 
tance of 2 feet would cause a torque of 100 lbs. -ft. 

The most common method of testing the mechanical output 
of a motor is with the Prony brake. Fig. 378. The brake con- 
sists of a lever arm of wood hollowed out to fit the pulley and 
clamped to it by bolts passing through a wooden block on 
the other side of the pulley. The bolts are fitted with wing 
nuts, by means of which the pressure on the surface of the 
pulley can be adjusted, thus altering the force due to friction, 
and the pull at the end of the lever arm. By measuring this 
pull, the speed of rotation, and the length of the lever arm, the 
power developed can be readily calculated. 

Method. — The principle of the brake is quite simple, for it is evident 
that due to the friction of the clamp on the motor pulley there is a tend- 
ency to make the lever arm rotate. The tendency to rotate is measured by 



DIRECT-CURRENT MOTORS 449 

means of a platform scale, the lever arm resting on a V-block on the plat- 
form of scales, or by means of a spring balance as in Fig. 378, the direction 
of the balance being perpendicular to the brake arm. Work is equal to 
the product of force and distance, that is, W = F x r, ][ 138, where r is 
the distance from the center of the shaft 

to the point of apphcation of the force (S) 

resisting the tendency of the lever to [f| 

rotate. In one revolution of the pulley, U 

the brake arm if allowed to rotate with V 

it would describe a circle having a c:;;|p o^p p <^ 

radius r feet (length of arm. Fig. 378), 
the distance then through which the 
point of application of the force would 
travel would equal 27r x r,^ and if the 
number of revolutions per minute is n, 
the power, in foot-pounds per minute. Fig. 378. — Prony Brake, 

is Power = 2 tt r n F, where F equals 

the force of the pull in pounds. To reduce this to horse-power, it is neces- 
sary to divide by 33,000, since one mechanical horse-power equals 33,000 ft.- 
Ibs. of work per minute (^ 139), or 

^ 2 7rrnF ^ 

33,000 ^ ^ 

In testing the output of large motors, they are coupled to 
available generators, the output of which is absorbed by suit- 
able resistances. If the generators happen to develop the same 
voltage as that of the circuit supplying the motor the current 
from the generators may be returned to the supply circuit, 
thereby saving considerable power. The amount of load in 
this method, called the loading-back method, is regulated by 
altering the strength of the generator fields. 

316. Output and Efficiency of Motors. — The capacity of 
a motor to perform useful work is limited by the same condi- 
tions as those governing the capacity of a generator, ^ 306. 
Motors are commercially rated according to the amount of 
power they will maintain at full load, at their pulleys, within 
the hmit of permissible heating. For example, a 10-kw. 110- 
volt motor will, when supplied with 110 volts at its terminals, 
develop 10 kw. or 13.4 horse-power at the pulley. The effi- 
ciency of a motor, as in the case of the generator, ^ 309, is 

1 The Greek letter ir (pi) represents the relation between the diameter 
of a circle and its circumference, and is equal to 3.1416. Circumference of 
a circle = tt x d, where d is the diameter. 



450 LESSONS IN PRACTICAL ELECTRICITY 

the ratio of the output to the input. The energy furnished to 
the motor is readily measured, and from this must be sub- 
tracted the losses in the motor to obtain the available energy. 
These losses are divided into two classes: the I^R losses in the 
armature and fields, and the stray power loss, which includes 
friction, eddy currents and hysteresis. Therefore, 

^ . output input — losses /-.^„^ 

efficiency = . ^ = -^ — ^ (107). 

input input 

Consider a 25-H. P., 220-volt, shunt-wound motor, having 
an armature resistance of 0.1 ohm and a field resistance of 
80 ohms, to operate under heavy load. Its speed at this load 
is such as to develop a counter E. M. F. of 210 volts. The 
drop in the armature is the difference between the applied 
voltage and the counter E. M. F., or 220 - 210 = 10 volts. 
The armature current is 10 -^ 0.1 = 100 amperes, and the field 
current is 220 -j- 80 = 2.75 amperes. The power consumed in 
copper loss is 10 x 100 = 1000 watts in the armature and 
2.75 X 220 = 605 watts in the shunt field. If the stray power 
loss be taken as 600 watts, then the total loss in the machine is 
1000 + 605 + 600 = 2205 watts. 

The input to the motor is 100 x 220 = 22,000 watts for the 
armature and 605 watts for the field, or a total of 22,605 watts. 
Whence the efficiency by Formula (107) is 

^ . 22,605 - 2205 20,400 ^ ^^^ ^^ ^ ^ 

^^^^^^^^ = 22,605 = 2W5 = '-'"' = ''-' ^- 

rr.! X XX- 20,400 ^^ , , 20,400 o^ . TT T^ 

The motor output is ~— r = 20.4 kw. or ~^-—- = 27 A H. P. 
1000 746 

317. Starting Motors. — The resistance of the armatures 
of motors is very low; for example, the armature of the 220- 
volt 25-H. P. shunt motor of H 316 has a resistance of 0.1 ohm. 
If this motor were directly connected to the supply mains, a 
much greater current than that required for full load would 
flow through it before any counter E. M. F. could be developed, 
resulting in damage to the windings; the low resistance would 
practically short-circuit the mains, causing an excessive drop of 
voltage. See Problem 128. For this reason a rheostat, called a 



DIRECT-CURRENT MOTORS 



451 



fMOM 



starting box, Fig. 379, is always inserted in the armature circuit 
of a shunt motor to limit this current before the motor attains 
its speed. The value, of resistance in the starting rheostat 
should be such that, when added to the armature resistance, 
it would permit the motor to take a 
current not much larger than its full- 
load value. As the motor attains some 
speed, and counter E. M. F., this re- 
sistance is gradually cut out by moving 
arm S from post 1, to 2, to 3, etc., 
until at point 5 the armature is directly 
connected across the line. For.example, 
to start the shunt motor, close switch A, 
when the motor fields will be excited; 
move the arm S of the starting box to 
point 1, when the armature circuit will 
be completed through the starting re- 
sistance; cut out the starting resistance 
as the motor attains speed by gradually 
moving S to point 5. To stop the 
motor, open the main switch A, and 
then place the arm of the starting box 
on the off-position, so that the motor 
will be ready for re-starting. 

In an automatic motor starting box, 
such as that depicted in Fig. 65, the 
arm S carries a. small piece of iron, 
shown at P in Fig. 379, and turns 
against the action of a spring; an 
electromagnet M, in series with the 
shunt field, is mounted on the box, and 
when arm S rests on point 5 it is held there by the electromagnet 
against the action of the spring. The advantage of this arrange- 
ment is that, if for any reason the main power supply circuit 
should be interrupted, the starting box arm will automatically 
open the circuit and shut down the motor, instead of permitting 
the motor armature to cause a short-circuit across the mains 
when the power is again turned on. 

In starting a shunt motor always be sure that the fields are first 




^j)smsL^ 



Fig. 379. — Connections 
of a Shunt Motor to a Gen- 
erator Circuit. 



452 



LESSONS IN PRACTICAL ELECTRICITY 



excited (test their attractive power with a penknife), since 
without the field excitation the armature, in its efforts to gen- 
erate a counter E. M. F., would speed up to a dangerously 
high value and possibly be wrecked. 

Series motors are also equipped with starting resistances, in 
the form of a controller, which is gradually moved to cut out re- 
sistance, as with shunt motors. 

318. Speed Control of the Shunt Motor. — In many motor 
applications it is necessary to alter the speed of the motor. 




Fig. 380. — Wiring Diagram of Four -pole Interpole Motor. 

(Interpole coils are in series with the armature. 

This is usually accomplished in shunt motors by varying the 
strength of the magnetic field. Sometimes in experimental 
work a variable resistance is introduced into the armature 
circuit, but this method of speed control is wasteful of energy 
and speed changes occur with variations of load. Again, the 
speed of shunt motors may be changed by altering the E. M. F. 
impressed upon the armature. This method is employed in 
machine shops for driving lathes, planers, drill presses, etc., 
and requires multi-voltage supply circuits. 

Returning to the usual method of speed control, namely 
magnetic field variation, it must be remembered that the stronger 
the field the lower will be the speed necessary for the develop- 



DIRECT-CURRENT MOTORS 



453 



ment of counter E. M. F. for a given load. To make a shunt 
motor speed up it is necessary to weaken its field. The strength 
of the magnetic field may be varied, 1, by altering the current 
in the field coils, and 2, by altering the magnetic reluctance 
of the path of lines of force. 

1. The current in the field coils can be varied by placing a 
rheostat in the field circuit. Increasing its resistance lessens 
the current and weakens the field, and consequently the motor 
speeds up. The control of speed by varying the field strength 
is limited in range of action, 
since on one hand saturation 
of the magnetic circuit re- 
quires large field currents 
which cause undue heating, 
and on the other hand, with 
low field strengths, armature 
reaction produces a con- 
siderable demagnetizing and 
distorting effect on the field 
flux and occasions sparking. 
However, the range can be 
vastly improved by neu- 
tralizing the effects of ar- 
mature reaction, If 296, by 
means of compensating windings and interpoles. Fig. 380 shows 
the connections of an interpole (or commutating-pole) motor. 
Such interpole or compensated motors afford sparkless commuta- 
tion under wide ranges of speed and load, and are splendidly 
adapted for individual motor drive of machine tools, for elevator 
operation, for driving printing presses, and for many other 
applications where large speed variations are essential. 

A combined starting and field-regulating rheostat is shown in 
Fig. 381. The movable arm has two parts which wipe over 
separate sets of contacts. The motor is started by moving the 
handle to the extreme right, where the magnet will hold one 
part of the arm. The other part is then moved back and will 
make contact with the studs connected with the field resis- 
tance and thus alter the speed of the motor to any desired 
value. 




Fig. 381. — Combined Starting Box 
and Field-regulating Resistance. 

Cutler-Hammer Mfg. Co. 



454 LESSONS IN PRACTICAL ELECTRICITY 

2. The speed of a shunt motor may be varied by altering the 
reluctance of the path of flux, usually by varying the length of 
the air gap between the armature and the field poles. Increas- 
ing the gap length, decreases the flux and therefore produces a 
higher speed. This method is utilized in motors made by the 
Stow Manufacturing Company, in which the iron poles are 
simultaneously moved through hollow field cores by means of a 
hand wheel. It is also utilized in motors made by the Reliance 




Fig. 382. — Reliance Adjustable-speed Motor. 

Electric and Engineering Company, in which the width of the 
air gap is different at the two ends of the machine, and speed 
variation is accomplished by an axial movement of the armature 
with respect to the field. Fig. 382 shows a Reliance semi- 
enclosed motor in which the speed is adjusted by moving the 
armature by the hand wheel. 

319. Speed Regulation. — The speed of a shunt-motor under 
constant impressed voltage and fixed excitation will be approxi- 
mately constant. The speed will fall somewhat as the load on the 
machine is increased because of the increased armature drop. 
This change of speed, with a definite setting of the field rheo- 
stat, occurring from full load to no load, expressed as a per- 
centage of the speed at no load, is called the speed regulation 
of the motor. 

c, , , ^. no-load speed - full-load speed ' ,.,^ox 

Speed regulation = — — — ^ — . . (108). 

no-load speed 



DIRECT-CURRENT MOTORS 



455 



Speed regulation concerns itself with changes in speed inherent 
in the machine, whereas speed control signifies deliberate 
external adjustment to attain various desired speeds; care 
should be exercised not to confuse these terms. 

Problem 130. — A motor when operating at full load runs at 1700 rev. 
per min. and when the load is removed its speed is 1800 rev. per min. 
What is its speed regulation? 



By Formula (108), 



speed regulation 



1800 - 1700 
1800 



0.056 = 5.6%. 



When the numerical value of the speed regulation of a motor is 
small, as in the foregoing problem, the motor is said to possess 
good speed regulation. 

Series motors operated from constant-potential mains are 
distinctly variable-speed motors. They have a low speed under 
large load and a 
high speed under 
light load. If the 
load were removed 
from a series motor 
it would speed up 
tremendously and 
perhaps be ruined ; 
such motors are 
consequently sol- 
idly coupled to 
their loads, by 
gears rather than 
belts. Fig. 383 
depicts a Type 

CO2-500 General Electric Co. series-wound, reversible, totally- 
inclosed motor for operating cranes and hoists. It is equipped 
with a shoe-type solenoid brake for holding the load at any 
position. 

320. Characteristic Curves of Motors. — In selecting a 
motor for performing a definite service it is desirable to know 
its performance characteristics at various loads. In shunt 
motors one is interested in the speed, current input, torque 
exerted, and efficiency for various outputs, and this information 




Fig. 383. — Series- wound Crane Motor. 

Made in sizes up to 240 H.P. 



456 



LESSONS IN PRACTICAL ELECTRICITY 



is usually embodied in curves plotted on cross-section paper and 
supplied by the manufacturer. Fig. 384 shows the characteristic 
curves of a 7.5-H. P., 230-volt, Type RC General Electric Co. 
commutating-pole shunt motor. Illustrations of this machine 
are given in Figs. 375 and 376. 



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Fig. 384. — Characteristic Curves of a Shunt Motor. 
Reading from this curve for only three different loads, 



Load 


Current 


Torque 


1^ % full load 


7.7 amperes 
14.1 " 
27.5 


11 Ib.-ft. 


50 % " '' 


23 " 


100 % " " 


47 " 







it is seen that both the current and the torque of this shunt 
motor increase nearly proportional to load. Per ampere of 

current there is produced a torque of — = 1.4 Ib.-ft. at \ load, 

^ = 1.6 Ib.-ft. at \ load, and ^~- = 1.7 Ib.-ft. at full load; 
14.1 ^7.0 

showing that the torque exerted by the motor is very nearly 
proportional to the current taken. 



DIRECT-CURRENT MOTORS 



457 



The series motor presents quite different characteristics for 
it was stated in ^ 319 that with increased load the speed of a 
series motor decreases. This is shown in Fig. 385, which gives 
the speed, torque, and efficiency curves of a GE-247 commu- 
tating-pole, 600- volt, 40-H. P. (one-hour rating ^) series rail- 







































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ftmperes 

Fig. 385. — Characteristic Curves of a Series 
Railway Motor. 

Diameter of car wheels is 30 in. ; gear ratio f | = 4.2. 

way motor. This motor is illustrated in Fig. 386. The torque 
curve is marked tractive effort in the diagram, tractive effort 
being the force exerted by a railway motor on the car in the 

^ Nominal rating of a railway motor is the mechanical output at car 
axle which causes a temperature rise above surrounding air, by ther- 
mometer, not exceeding 90° Centigrade at the commutator and 75° Centi- 
grade at any other normally accessible part after one hour's continuous 
run at rated voltage on a stand with the motor covers arranged to secure 
maximum ventilation without external blower. 



458 



LESSONS IN PRACTICAL ELECTRICITY 



direction of its motion. The relation between tractive effort 

in pounds and torque in Ib.-ft., neglecting losses in gears, is 

given by 

24 X gear ratio X torque /1AQ^ 

. . (109). 



tractive effort 



wheel diameter in inches 



The relation between car speed in miles per hour and motor 
speed in rev. per min. is given by 

torque X motor speed 



miles per hour = 



14 X tractive effort 



(110). 



Reading tractive effort and speed from the curve for three 
current values, 



Current 


Tractive Effort 


Speed 


25 amperes 

60 " 


250 lbs. 

1000 " 

1700 " 


24.9 miles per hr. 
15.2 " " " 


90 


12.5 " " " 







it is seen that small torque is exerted by a series motor at 
high speed and vice versa. Since power output equals the 

product of torque 
and speed, the series 
motor draws a more 
uniform amount of 
energy from the line 
than does the shunt 
motor. Thus, from 
the foregoing table, 
while the tractive 
effort varies from 
250 to 1700 lbs., a 
7-fold increase, the product of tractive effort and speed increases 
from 6230 to 21,200, a 3.5-fold increase of power. On the 
other hand, a shunt motor would demand a 7-fold increase of 
power. For this reason the series motor is particularly well 
suited for car propulsion and for the operation of cranes, hoists 
and rolling mills. 




Fig. 386. — Series Railway Motor GE-247. 

Frame has bearing in front which ruhs on wheel 
axle. Gear case is shown at the right. 



DIRECT-CURRENT MOTORS 459 

Compound-wound motors in which the series and shunt fields 
assist each other are frequently used for heavy intermittent 
loads, such as in operating elevators, rolling mills, etc. They 
exert a powerful starting torque and yet the speed is not exces- 
sively variable under load variations. 

321. Electric Traction. — Series motors are used for rail- 
way work because they best fulfill the requirements, namely 
powerful torque at starting, variable speed and economical 
operation at varying loads. When two motors are used on 
a car their armatures and field coils are connected in series 
with each other and a resistance, which prevents too great a 
rush of current from the mains when the car starts. As the 
car gains headway a rheostat and switch, termed a series- 
parallel controller gradually cuts the resistance out of circuit' 
until the motors operate in series on full voltage, then places 
the motors in parallel with a resistance in series with both, then 
gradually cuts out this resistance step by step until, finally, it 
connects each motor directly across the mains, or between the 
overhead trolley and the track; one terminal of the station gen- 
erator being connected to the trolley and the other to the track. 

On a level road the tractive effort to be exerted by a motor 
in order to drive the car at constant speed varies with a number 
of conditions, such as road bed, track, lubrication of journals, 
wind pressure, etc., collectively considered as train resistance. 
The tractive effort varies directly as the weight of the car with 
passengers. For average conditions about 20 pounds tractive 
effort are required for each ton propelled by the motor on a 
level road, with a speed of from 20 to 40 miles per hour. For 
example, to propel a car weighing 20 tons, with passengers 
aboard weighing 3 tons, will require a tractive effort on a level 
of (20 + 3) X 20 or 460 pounds. In general the tractive effort in 
pounds to be exerted by a motor in propelling a car of W tons 
weight against train resistance is 

tractive effort (resistance) = 20 W (111). 

When the car ascends a grade a certain amount of addi- 
tional energy is required to propel it, and this is represented by 
the amount of energy required to raise the car through the 
distance it travels vertically. 



460 LESSONS IN PRACTICAL ELECTRICITY 

Grades are designated by the rise in feet per 100 feet traveled; 
thus a 4 % grade means a vertical rise of 4 feet in a hori- 
zontal distance of 100 feet. The tractive effort which is neces- 
sary to propel each ton of car weight up a one per cent grade 
is T^TT X 2000 = 20 pounds, consequently if a car of W tons 
weight is to be drawn up a grade of g per cent with uniform 
speed then the tractive effort in pounds is 

tractive effort (grade) = 20 Wg (112). 

The greatest amount of force required in railway operation 
however, is th^^t necessary to accelerate the car from standstill. 
It takes a tractive effort of about 100 pounds to accelerate each 
ton of car weight at the rate of 1 mile per hour per second. 
Therefore to accelerate a car of W tons weight at the rate of A 
miles per hour per second requires a tractive effort (in pounds) of 

tractive effort (acceleration) = 100 WA .... (113). 

Consider a 20-ton car equipped with two series motors of the 
type shown in Fig. 386, whose characteristic curves are presented 
in Fig. 385. If this car shall start on a level track with a 
velocity increase every second of 1.5 miles per hour then a 
tractive effort is required which, by combining Formulas (111) 
and (113), is 

tractive effort = 20 X 20 + 100 X 20 x 1.5 = 3400 pounds. 

Each motor must exert half of this or 1700 pounds, which from 
Fig. 385 demands a current of 90 amperes. This current may 
be kept fairly constant by the controller while the car is acceler- 
ating until the two motors are each operating on the full line 
voltage of 600, which occurs when the speed of the car is 12.5 
miles per hour (from same diagram). Thereafter the speed 
increases less rapidly because the current decreases as the car 
speeds up and this results in a lower available tractive effort; 
this reduction of the acceleration rate continues until even- 
tually the speed of the car becomes constant. This constant 
speed will be that for which the available tractive effort is" 

20 X 20 
equal to the train resistance per motor, which is — - — = 200 

pounds, the speed being 27 miles per hour, Fig. 385. 



DIRECT-CURRENT MOTORS 461 

322. Direct-Current Motor-Generator Sets. — For some pur- 
poses two (and sometimes more) dynamos are firmly coupled 
together as a unit, one machine acting as a motor and the other 
as a generator. Motor-generator sets may comprise, 1, direct- 
current machines, 2, alternating-cm-rent machines, and 3, 
both direct- and alternating-current machines. The first class 
includes balancers for maintaining the potential of the middle 
wire of three-wire systems, and voltage-changing sets for battery 
charging, electrolytic work, welding, voltage boosting, etc. The 
second and third classes are considered in ^ 375, Lesson XXX. 




330 Voli 
Oeneraior 



Fig. 387. — Motor Generator Used as a Balancer on 
a Three-wire Circuit. 

A balancer associated with a three-wire distribution cuxuit 
is shown in Fig. 387 with its two dynamos connected in series 
across the generator leads. If the circuit is unbalanced and 
supplies a heavier load on say the upper side, the voltage on 
the lower side tends to become higher than on the other and 
the lower dynamo of the balancer will operate as a motor and 
drive the upper dynamo as a generator, which then assists in 
supplying current to the greater load on the upper side; this 
action takes place automatically. These machines usually 
have shunt or compound excitation and are rated by the amperes 
carried in the neutral wire. 



QUESTIONS 

1. How does a motor differ from a generator? 

2. What is the difference between a shunt and a series motor? 

3. A series generator rotates clockwise. What will be the direction 
of rotation when it is used as a motor? 



462 LESSONS IN PRACTICAL ELECTRICITY 

4. A shunt generator runs in a counter-clockwise direction. How 
will it run when driven as a motor? 

5. What change is necessary in order to run the shunt dynamo in 
Question 4 as a motor in a clockwise direction? 

6. Since the counter E.M.F. of a motor permits less current to flow 
through it than if it did not exist, and the turning effort of a motor depends 
on the current through the armature, of what advantage then is the counter 
E. M. F.? 

7. State two methods by which you can prove a motor to possess 
counter E. M. F. 

8. Upon what factors does the counter E. M. F. depend? 

9. A shunt motor is called a constant-speed motor; how is it possible 
then for the motor to take current from the line in proportion to the 
power it develops, since if it always runs at constant speed the counter 
E. M. F. would be constant, and therefore the current constant? 

10. Why is it impossible for the counter E. M. F. of a motor to attain 
a value equal to the appHed E. M. F.? 

11. What is meant by the speed regulation of a motor? 

12. Explain the function of a starting box. 

13. What are some uses of motor-generator sets? 

14. What factors determine the mechanical power which can be exerted 
by a motor? 

15. What is meant by motor torque? 

16. State the conditions of torque and speed that motors are required to 
develop in commercial work, and the kind of motor adapted to each case. 

17. Explain two methods of speed control of shunt motors. Illustrate. 



PROBLEMS 

1. A shunt motor having an armature resistance of 2 ohms and a 
field resistance of 125 ohms is connected to 250-volt mains and develops 
a counter E. M. F. of 220 volts. What current is taken from the line? 
Ans. 17 amperes. 

2. What mechanical power is developed by the motor in Problem 
1? Ans. 4:A H. F. 

3. If there are 500 watts lost in mechanical friction, hysteresis and 
eddy currents in the motor in Problem 1, what useful power can the motor 
develop? Ans. 3.7 H. P. 

4. What is the efficiency of the motor mentioned in the above problem? 
Ans. 65 %. 

5. A small shunt motor runs at 1400 rev. per min. when connected to a 
220-volt circuit. When driven as a generator it generates 220 volts P. D. 
at a speed of 1600 rev. per. min. What is the counter E. M. F. when the 
machine is used as a motor? Ans. 192.5 volts. 

6. The resistance of the armature in Problem 5 is 1.45 ohms. What 
current flows through it when the machine is run as a motor at 1400 rev. 
per min.? Ans. 19 amperes. 



DIRECT-CURRENT MOTORS 463 

7. The field of the motor in Problems 5 and 6 receives 3 amperes. 
If 300 watts are required for mechanical losses, what is the efficiency? 
Ans. 70 %. 

8. In making a brake test on a motor, the lever arm used is 3 feet long 
and the motor runs at 1150 revolutions per minute when exerting a pull 
of 25 pounds, (a) What is the motor torque? (6) What H.P. is developed? 
Ans. (a) 75 Ib.-ft. (b) 16.4 H. F. 

9. The counter E. M. F. of a motor is 230 volts; the current through 
the armature 25 amperes, its resistance 0.4 ohm. What is the applied 
E. M. F.? Ans. 240 volts. 

10. Determine the speed regulation of the shunt motor whose charac- 
teristic curves are given in Fig. 384, taking the no-load speed as 890 rev. 
per min. Ans. 5 %. 

11. What tractive effort must be exerted by the two motors of a 15-ton 
trolley car in order to accelerate the car on a 1.5 per cent grade at the 
rate of 1.2 miles per hour per sec. Ans. 1275 pounds each. 

12. If motors whose characteristic curves are shown in Fig. 385 are 
used on the car of the preceding problem, (a) what current will each 
motor take during acceleration? (b) What is the ultimate speed on the 
grade? Ans. (a) 72 amperes, (b) 21.5 miles per hour. 



LESSON XXVII 

ELECTRIC LIGHTING 

Arc Lamps — Flaming Arc Lamp — Special Forms of Arc Lamps — 
Mercury Vapor Lamp — Incandescent Lamps — Lamp Filaments — 
Commercial Rating of Incandescent Lamps — Efficiency and Life of 
a Lamp — Table XIX — Light Distribution Curves — Incandescent 
Lamp Circuits — Potential Distribution in Multiple-Lamp Circuits 
— Loss on Line Wires — Incandescent Wiring Calculations — The 
Three-Wire System — Motor Wiring Calculations — Installation of 
Interior Wiring — Questions and Problems. 

323. Arc Lamps. — When an electric current under a pressure 
of about 45 volts, is passed through two carbon rods, with their 
ends first in contact and afterward gradually separated a short 
distance, as one-eighth inch, a brilliant arc of flame called the 
electric arc, is established between them. The high temperature 
caused by the passage of the current through the resistance of 
the contact surfaces causes the carbon to vaporize 

tand the vapor thus arising, being a much better 
conductor than the air, conducts the current across 
the gap from one carbon tip to the other. As the 
arc is maintained across the gap, disintegration of 
III- the carbon takes place, the carbons waste away, 
and a cup-shaped depression, termed the crater, is 
Fig. 388. — formed in the positive carbon, while the tip of the 
Electrodes. negative carbon assumes a conical form, Fig. 388. 
Both carbons waste away, but the consumption of 
the positive carbon is about twice as rapid as that of the nega- 
tive, since most of the vapor comes from the positive carbon 
and part of that vapor is deposited as graphite on the negative 
cone-tipped carbon. 

If the rods are composed of pure carbon the greater part of 
the light is emitted by the glowing tips of the rods, and but little 
by the incandescent carbon vapor ; most of the light comes from 
the " crater " formed in the upper or positive carbon, Fig. 388. 

464 



ELECTRIC LIGHTING 465 

The light is largely thrown downward and has the greatest 
intensity at an angle of about 45° below the horizontal. In an 
alternating arc lamp, the crater alternates from one carbon to 
the other with each reversal of current, so that both carbons 
are consumed about equally, the light being emitted from both 
carbon tips with about equal intensity. 

In commercial arc lamps automatic regulation is employed 
to feed the carbons as they are consumed, and thereby main- 
tain the proper length of arc required. This is accomplished 
by a suitable arrangement of mechanical movements actuated 
with solenoids. The arrangement of solenoids gives rise to 
several different types of lamps for operation on series circuits 
and on multiple circuits. Lamps to be operated in series gen- 
erally have a solenoid connected in series with the two carbon 
rods and another solenoid of much higher resistance is con- 
nected in shunt with the arc. Both coils act upon a hinged 
armature which controls a clutch that engages a rod carrying 
the upper carbon. The carbons are in contact when the lamp 
is not in use, and when the current is turned on the series sole- 
noid is energized and the upper carbon is raised the proper dis- 
tance, thus '^ striking " the arc. As the carbons are consumed 
the length of the arc gap and its resistance increases, which 
causes more current to flow through the shunt solenoid; when 
this current reaches such a value that the attractive force 
for the armature controlling the feeding mechanism overcomes 
the attractive force of the series solenoid, the action lowers 
the upper carbon to its former distance from the lower carbon. 
The two solenoids act in opposition to each other, this method 
of regulation being known as the differential method. 

The feeding mechanism of arc lamps used on constant- 
potential multiple circuits may be controlled by a solenoid 
connected in series with the carbon rods. The solenoid actuates 
the mechanism controlling the clutch that grips the rod carrying 
the upper carbon. As the carbons are consumed, the gap length 
and resistance is increased, thus lowering the current and attrac- 
tive force of the solenoid; soon the clutch releases the upper 
carbon rod, allowing it to drop and touch the lower carbon 
rod, at which moment the solenoid action raises the upper rod 
to the proper distance for the arc. 



466 



LESSONS IN PRACTICAL ELECTRICITY 



In all multiple lamps a balancing coil, which is a resistance for 
direct-current lamps and may be a reactance coil for alternating- 
current lamps, is connected in series with the arc; its object is 
to adjust the voltage across the arc and steady the current. 

The open arc lamp, which was used many years ago for street 
lighting, was later replaced to a great extent by the enclosed arc 
lamp, operating in series on a constant-current 
circuit. The enclosed arc lamp was until re- 
cently used to a great extent for indoor lighting, 
as in stores and factories, etc., and operated in 
multiple on constant-potential circuits. (Since the 
introduction of the gas-filled metal-filament in- 
candescent lamps, 1[ 328, thousands of these en^ 
closed arc lamps both for indoor and street light- 
ing have been replaced by large-size incandescent 
lamps.) There are, therefore, series or constant- 
current lamps and multiple or constant-potential 
lamps; either type being adapted to direct or 
alternating current and using the methods of 
regulation just described. Arc lamps for street 
lighting are usually operated in series on constant- 
current circuits because the lamps are distributed 
over a large area and the energy can be more 
economically supplied at a high pressure and a 
small current. 

In the so-called enclosed arc lamp using carbon rods, the 
'' arc " is enclosed in an almost air-tight inner glass globe, 
so designed that just enough air is admitted to prevent the 
free carbon dust coming from the arc from being deposited on 
the inside of the bulb. By excluding all but a very small 
amount of oxygen the consumption of the carbons is dimin- 
ished and the length of the arc increased to about f inch; with 
the increased length of arc the potential across the arc is in- 
creased to about 80 volts. The chief advantages of enclosed 
arc lamps over the old open arcs are the saving of carbons 
and the diminished cost of labor for trimming. An open arc 
lamp having one set of carbons will burn from 8 to 10 hours, 
while an enclosed lamp will burn about 150 hours on direct 
current and about 100 hours on alternating current. A 6.6- 




Fig. 389. — 
Interior of an 
Enclosed Arc 
Lamp. 



ELECTRIC LIGHTING 



467 



ampere series direct-current enclosed arc lamp requires about 
500 watts and produces an average candle-power of 260. . An 
interior view of an enclosed arc lamp with its inner globe is 
shown in Fig. 389. 

324. Flaming Arc Lamp. — In the carbon arc lamps, described 
in 1[ 323, practically no light is given out from the arc itself, the 
light being produced by the incandescence of the carbon ter- 
minals. In the flaming arc lamp carbon electrodes are used 
having a core made up of a mixture of powdered carbon, mineral 
salts and a suitable binder. The presence 
of mineral salts in the carbon produces 
between the arc terminals a vapor path 
conveying the particles of light-producing 
substances. Owing to the presence of these 
substances in the arc, the temperature of the 
carbon is reduced, so that they produce very 
little light, and nearly all of the illumination 
comes from the arc flame. Flame arc lamps 
are also constructed on the principle of the 
ordinary enclosed carbon arc lamps in that 
the arc is enclosed in a glass chamber to 
which the supply of air is limited by an ar- 
rangement of air-circulation and condensing 
chambers in which the fumes deposit. The 
enclosed flame arc lamp, Fig. 390, shares the 
advantages of the open flame arc lamp in 
high candle power and efiiciency but lacks most of its objection- 
able features. 

In most open flaming arc lamps, both carbons are fed point 
downward at an angle to each other, thus obtaining maximum 
illumination without interference and shadows. Some flaming 
arcs, however, particularly of the enclosed type, have the carbons 
arranged in a vertical line, as in the ordinary arc. The lamp 
requires about 45 to 70 volts at the arc and from 8 to 10 am- 
peres. Flaming arc lamps, because of their very high candle- 
power, are best suited for the lighting of large areas, as in 
street illumination, or for display and advertising purposes. 
These lamps are rarely used for indoor lighting because of the 
obnoxious fumes given off. 




Fig. 390. — En- 
closed Flame Arc 
Lamp. 



468 



LESSONS IN PRACTICAL ELECTRICITY 




Fig. 391.— 
Magnetite Arc 
Lamp. 



The Magnetic Arc Lamp. — The magnetite arc is so called 
because it uses magnetite, one of the oxides of iron, as the 
negative electrode, the magnetite being in the 
form of powder and tightly packed in a steel 
tube. The positive electrode is copper. In one 
type of this lamp the negative electrode is 
placed at the top and in another at the bottom. 
The magnetite lamp (Fig. 391) has a white 
dazzling flame arc of great intensity but small 
volume. The lamp is particularly adapted for 
street lighting, since, owing to the slow con- 
sumption of metal in the arc, frequent trimming 
is not required. A standard type of lamp for 
street lighting requires a direct current of 4 
amperes and 78 volts at the arc; its mean 
spherical candle-power is 250. It is objection- 
able for indoor hghting because of the fumes 
which are given off during the consumption of 
the metallic electrode. 
325. Special Forms of Arc Lamps. — Arc lamps of an 
entirely different form from those used for general lighting are 
designed for use in focusing lamps and in search-lights. 

Focusing lamps are used for picture projection, " spot lights" 
and motion pictures. In these lamps the carbons may be fed by 
hand or automatically by means of a solenoid. In some pro- 
jection lanterns the carbons are placed end to end, in a straight 
line that is tilted or inclined at an angle of about 25° to the ver- 
tical, the axis of the lower carbon, however, being slightly in 
advance of the upper or positive carbon, A, Fig. 392, in order 
to throw as much light as possible toward the condensing 
lenses of the lantern. 

The carbons in arc lamps used in some forms of stereopticons 
are arranged at right angles to each other as shown at C, 
Fig. 392. This arrangement has the advantage of giving more 
light for the same amount of direct current than the tilted form, 
and of keeping the arc centered for a greater length of time, 
without readjusting the carbons. 

In the hand-feed lamps, the carbons are fed toward each other 
by a hand-operated screw feed, and as the positive carbon of a 



ELECTRIC LIGHTING 469 

direct-current arc is consumed at a faster rate than the negative, 
the mechanism is so arranged that the upper or positive carbon 
is moved twice as fast as the other, in order to keep the crater 
at the correct point for the desired hght projection. 

With arcs to be operated on alternating currents, two craters 
are formed, and to use the hght from both requires a very care- 
ful setting and adjustment of the carbons so as to avoid poor 
illumination. The carbons are generally cored and are fre- 
quently set as shown at B, Fig. 392. 

In arc latnps for motion picture work, the carbon holders are 
designed to accommodate carbons of f inch to J inch in diameter, , 
with the upper carbon 12 inches in length and the lower 6 inches 





Fig. 392. — Arrangement of Carbons in Focusing Lamps. 

in length; the arc takes a current of 75 to 100 amperes. The 
lamp adjustments are so designed that the carbons may be 
placed at any angle desired, they can also be moved forward, 
backward and sideways independently of each other, or the 
whole lamp can be swung backward, laterally, or up and down. 
When operating such arcs on direct current rheostats are re- 
quired to regulate the voltage so as to obtain proper results; 
where alternating current is used the best results are obtained 
by using a transformer that will reduce the pressure of the 
commercial circuit to about 30 or 35 volts, the voltage at which 
the hand-feed open arc is generally operated. 

In arc lamps designed for search-light projectors the carbons 
may be either inclined or horizontal; the arc, however, is always 
directed towards the reflector and away from the object to be 
illuminated. In search-lights where it is desired -to have the 



470 LESSONS IN PRACTICAL ELECTRICITY 

light cover a large area, dispersion lenses are used which dis- 
perse or spread out the light beam in a conical shape. 

326. Mercury Vapor Lamp. — The mercury vapor lamp, 
Fig. 393, derives its light from the vapor of mercury in which 
the passage of an electric current causes a high state of incan- 
descence. The lamp consists essentially of a glass tube, several 
feet in length, exhausted of air. A platinum wire is sealed in 
each end of the tube, the wire at the positive end connects with 
a piece of iron and at the negative end connects with metallic 
mercury which forms the negative electrode. At starting, the 
resistance between the negative electrode and the vapor is very 




Fig. 393. — Mercury Vapor Lamp. 

high, and must be overcome before the lamp can be put in 
operation. Several methods are used to overcome this high 
resistance. 

In one method of starting the lamp a momentary high- 
potential discharge from an inductance coil is passed through 
the lamp, which at the same time is connected to the low- 
voltage mains. This discharge overcomes the high negative 
electrode resistance and the low-voltage current follows. In 
the modern lamps of this type an automatic device is used for 
suddenly breaking the circuit through the inductance coil, 
thereby inducing the high potential which starts the lamp. 
Fig. 394 shows the connections of the lamp in which this auto- 
matic starting device is used. The device is termed a '' shifter," 
and consists of an exhausted glass bulb containing mercury, 
which is actuated by an electromagnet M. When the circuit 
is first closed the current flows through the magnet M, the 




ELECTRIC LIGHTING 471 

resistance R, the inductance coil L, and the shifter S; but as 
soon as the magnet is energized the circuit through L is 
suddenly broken by the shifter. The self -inductance of coil 
L sets up a momentary high potential which causes a spark to 
jump from the auxiliary electrode B to the mercury at the 
negative electrode. This spark charges the mercury electrically 
and sets up sufficient vapor in the tube for the current to pass 
from P to N. The tube then glows with a light of a decided 
greenish hue, and with sufficient current, the high resistance will 
not again make its appearance until 
the current is turned off; when, if 
it is desired to relight the lamp, the 
same procedure must be repeated. 
The shifter, inductance, resistance, 
etc., are contained in a cylindrical 
metal box from which the glass tube 
is suspended. 

The simplest and least expensive Fig 394. — Connections of a 
.11^,,- xi 1 • • 1 Mercury Vapor Lamp, 

method 01 startmg the lamp IS Simply 

to tilt the tube until the two electrodes are brought in contact 
by a thin stream of mercury along the length of the tube and 
then allow the lamp to return to its normal position ; an arc is 
started by breaking the mercury stream, causing the volatiliza- 
tion of the mercury, the vapor filling the tube and producing 
light. 

The mercury vapor lamp is essentially a direct-current lamp. 
Lamps, however, are designed for operation on alternating- 
current circuits, such lamps being provided with two anodes, 
and an auto-transformer, ^ 357, the principle of operation being 
that of the mercury rectifier, ^ 367. 

The light produced by the mercury vapor lamp has a very 
penetrating effect, bringing out the shape and contour of 
objects very clearl}^, and for this reason the lamp is used to a 
great extent in photography, etc. A lamp about 4 feet in length 
and 1 inch in diameter would produce about 700 candle-power 
with a current of 3.5 amperes at 110 volts. A certain amount 
of inductance and resistance is usually placed in series with the 
lamp so as to counteract any effect caused by a variation in 
voltage and thus permitting the lamp to operate more steadily. 



472 LESSONS IN PRACTICAL ELECTRICITY 

327. Incandescent Lamps. — In an incandescent electric 
lamp the light is produced by heating to a state of incandescence, 
a high resistance solid conductor which is not readily fused by 
the passage of a current through it. The light-giving element, 
termed the filament, is hermetically sealed in a vacuum or in an 
inert gas within a glass bulb, to prevent it from burning. The 
material of which the filament is composed should have a high 
melting point and should not be liable to a rapid rate of evapo- 
ration at temperatures below the melting point. Increasing the 
temperature of a lamp filament increases the light given out 
much more rapidly than the energy needed to produce that 
temperature, but the rate of filament evaporation is also 
increased, therefore, the most efficient transformation of elec- 
trical energy into light is realized when the filament is operated 
at the highest temperature it can stand without causing exces- 
sive filament evaporation. Evaporation causes blackening of 
the glass bulb and results in a decrease in light from the lamp; 
it also naturally causes a gradual disintegration of the filament 
until it breaks. 

The filament is secured to two platinum wires sealed in one 
end of a glass tube; the platinum wires make connection with 
two copper wires which in turn connect to the lamp base, 
Fig. 69, page 73. Platinum is generally used for lead-in wires 
through the sealed glass tube because it expands and contracts 
at very nearly the same rate as glass, thus preventing the 
glass from breaking. The glass tube containing the lead-in 
wires and upon which the filament is mounted is sealed into 
the blown-glass bulb of the ordinary shape. The bulb is con- 
nected by means of a glass stem (which is left at the upper end 
of bulb when it is blown), to an air-pump and the air is ex- 
hausted; the stem is then heated near the bulb and sealed, 
forming the pointed tip on the end of the finished lamp. The 
lamp base consists of two pieces of brass insulated from each 
other, secured to the lamp bulb by cement, and arranged to 
hold the lamp securely when placed in a retaining socket con- 
nected to the supply mains. 

328. Lamp Filaments. — Carbon Filament — The car- 
bon filament is made in the following manner: absorbent 
cotton is dissolved in zinc chloride and hydrochloric acid, 



ELECTRIC LIGHTING 473 

forming a gelatinous mass a trifle thicker than molasses. 
This material is forced under pressure through a die, into a 
vessel containing alcohol which causes it to set and harden suf- 
ficiently for handhng, thus forming a long thread-hke filament. 
After washing, the material is wound upon a drum and dried, 
after which it possesses considerable strength. It is then gaged 
for size and cut into suitable lengths and wound upon forms 
to produce the required shape; thereafter the filaments are 
carbonized, by heating them in a furnace at a high temperature. 
The filament is next subjected to the ''treating" process, 
whereby a coating of graphitic carbon is deposited thereon by 
flashing in an atmosphere of hydrocarbon vapor; the object of 
which is to insure uniformity in resistance. The filament is 
then ready for mounting upon the platinum leading-in wires 
and is secured to them by a carbon paste. 

About 1907 an improvement was effected in the carbon fila- 
ment by a process termed " metallization," the filament being 
then called a metallized filament. This filament is produced by 
heating the ordinary carbon thread in an electric furnace 
before and after the " treating " process, giving it the appear- 
ance and electrical characteristics of a metal. The lamp con- 
taining this filament was placed on the market under the 
trade-name of the '' Gem " lamp, which, in appearance, is simi- 
lar to the carbon lamp. Fig. 395. The metallized filament has 
a positive temperature coefficient, that is, its resistance increases 
with an increase in temperature. The resistance of a filament 
changes by a certain percentage for each degree of tempera- 
ture change, which percentage is called the temperature coef- 
ficient, H 241. Lamps having positive temperature coefficients 
have their lowest resistance when cold, the ordinary carbon 
filament has a negative temperature coefficient, since its resis- 
tance is lowest when hot. The fact that metals have positive 
temperature coefficients accounts for the application of the term 
" metallized " to those carbon filament lamps having positive 
temperature coefficients. 

Since the introduction and perfection of the modern type of 
tungsten filament lamp the use of the carbon-filament lamp for 
general illumination has been decreasing and at present only 
7% of the total domestic lamp sales are for carbon lamps. 



474 



LESSONS IN PRACTICAL ELECTRICITY 



Tungsten Filament. — Tungsten or wolfram is a metallic 
element discovered in 1781 and named from the Swedish 
^' tung " (heavy) and " sten " (stone). It is not found native, 
but occurs as the tungstate of iron and manganese in the 
mineral " wolframite/' and as calcium tungstate. The pure 
tungsten metal comes in the form of a powder, is a bright steel 
gray, and is hard and very heavy. 

The first tungsten filaments manufactiired in this country 
were made similar to the carbon filaments, that is, the finely 






Gem Mazda B Mazda C 

Fig. 395. — Incandescent Lamps. 

Left — carbon filament lamp. Right — gas-filled tungsten lamp. 

Center — vacuum tungsten lamp. 

divided metallic tungsten was mixed with a suitable binder and 
squirted through dies into threads. The filament was then 
dried in an oven, after which it was placed in an electric fur- 
nace, the high temperature of. which readily removed the vola- 
tile parts. Thereafter an electric current was passed through 
it while within an atmosphere of inert gas, thus producing a 
thread of practically pure tungsten. Regardless of purity, the 
metal, however, still retained its brittleness, requiring careful 
handhng in the manufacture of the lamp and in its subsequent 
use. These early lamps (before 1910) were so fragile that they 
could only be used in the vertical position. 



ELECTRIC LIGHTING 475 

Improved methods were soon discovered for manufacturing 
tungsten in the form of drawn wire. The tungsten powder is 
pressed into ingots without a binder, and these are heated to a 
white heat in an electric furnace in an atmosphere of hydrogen, 
thus making them good electrical conductors. These ingots 
are then swaged and heated a number of times until reduced 
to a round rod sufficiently small to be drawn. This process 
takes place through diamond dies while the tungsten is very 
hot, the drawing being continued until the wire is of proper 
size. To this latest achievement in metal filament lamps the 
trade-name '' Mazda " has been applied, signifying the highest 
development in metal filament lamps. The production of 
tungsten wire in great lengths produced a change in the con- 
struction of the lamps, a continuous filament is now used instead 
of fusing four or five filament loops together as was done in the 
first tungsten lamps. The filament is now wound upon spiders. 
Fig. 395, the stiffer properties of the filament allowing longer 
loops without danger of interlocking. The tungsten wire is 
fastened to the leading-in wires, and the glass bulb exhausted 
of air to produce a vacuum, as in the carbon and Gem lamps. 
Of all filaments developed thus far, those made of tungsten 
metal have proven the most ideal for incandescent lamps. 
The tungsten filament lamp has a high positive temperature 
coefficient, a high efficiency, ^ 330, and produces a whiter light 
than the Gem lamp. In lighting installations where the fila- 
ment of the lamps come within the field of vision, it is customary 
to use lamps with the portion near the tip frosted; these are 
called bowl-frosted lamps. 

Gas-filled Tungsten Lamps. — The gas-filled tungsten 
lamp has its bulb filled with an inert gas, such as nitrogen, 
so that the tungsten wire filament can be operated at higher 
temperatures, and at higher efficiencies than the vacuum-type 
lamps. These lamps are known to the electrical trade as 
Mazda C lamps. Fig. 395, to distinguish them from the vacuum 
tungsten lamps known as Mazda B. The filament in the gas- 
filled lamps is wound in a coil of very small diameter and 
mounted in a compact manner upon small radial supporting 
arms projecting from the end of a long glass stem extending 
from the base. This construction concentrates the filament in a 



476 LESSONS IN PRACTICAL ELECTRICITY 

small space in the center of a pear-shaped glass bulb having 
a long neck. While the presence of the inert gas in the bulb 
tends to cool the filament by the passage of the rising gas, 
this effect is counteracted by using the compact form of fila- 
ment. The presence of the gas also reduces the rate of evapo- 
ration of the filament. Thus the lamp may be operated at 
even higher temperatures than is possible in the vacuum lamps. 
The hot gas currents also tend to carry any evaporated par- 
ticles to the upper portion of the bulb (base end of the lamp) 
where they can be deposited without interfering with the emis- 
sion of light. 

These gas-filled tungsten lamps have been most successful 
in the larger sizes, that is, from the 75-watt size up to the 1000- 
watt size; this is due to the fact that the larger-size filaments 
expose relatively less filament surface to the cooling effect of 
the gas than the smaller ones. Lamps of 500 watts and over 
have replaced thousands of arc lamps for the illumination of 
large areas indoors and for street illumination. With the 
compact form of filament they are used very successfully with 
reflectors for street-railway head-lights, for outdoor flood light- 
ing, for stereopticons and for small motion picture machines. 
Recently a 50-watt gas-filled lamp was introduced having a 
tipless bulb of white glass which conceals the filament from 
view. 

329. Commercial Rating of Incandescent Lamps. — Car- 
bon lamps were originafly rated according to the average 
intensity of light produced in a horizontal direction. The 
label on the lamp indicated the pressure, the watts consump- 
tion, and the corresponding candle-power. The standard 
carbon lamp once in general use was rated as equivalent to the 
light given by 16 candles, and consumed from 50 to 60 watts. 
A 110-volt, 55-watt, 16-c.p. lamp, requiring 0.5 ampere, had a 
resistance (hot) of 110 -^ 0.5 = 220 ohms. Carbon filament 
lamps were made for various voltages up to 220 volts. For any 
particular voltage the higher the candle-power of the lamp the 
larger was the cross-sectional area of its filament, the less its re- 
sistance, and, consequently, the more current it required. The 
filament of a 50-watt 110-volt carbon lamp is 9 inches long 
and 0.0040 inch in diameter. 



ELECTRIC LIGHTING 477 

All incandescent lamps are now rated in the total watts con- 
sumed, the rating in watts and the voltage at which the lamp 
is to be operated being indicated on the label of the lamp. The 
rating of the lamp in watts, instead of in candle-power, was 
decided upon for the reason that there are so many candle- 
power values that may be taken, that the latter rating was 
misleading and did not give the true comparison between the 
illuminants so rated. For example, the candle-power may be 
expressed as an average value in a horizontal direction (lamp 
axis vertical), or as a mean spherical value; in either case the 
values are greatly modified by the use of reflectors and shades. 
Moreover, the watt is the unit used in the rating of all current 
consumption devices, as electrical energy for power and light 
is measured and sold on a wattage basis. While the candle- 
power value is no longer indicated on the label of a lamp, its 
value may be derived from a knowledge of its efficiency; the 
mean horizontal candle-power of a lamp may be obtained by 
dividing the watt rating by the efficiency in watts per candle,. 
If 330. 

The metallized carbon filament (Gem) lamp for use on 110- 
to 125- volt multiple circuits is made in the following standard 
sizes: 20, 30, 40, 50 and 60 watts; while for 220- to 250-volt 
circuits the standard sizes are: 25, 40, 60 and 100 watts. 

The Mazda B tungsten lamp is made in 10, 15, 25, 40, 50, 
60 and 100-watt sizes for use in multiple circuits having volt- 
ages of] 110 to 125 volts; and in 25, 40, 60, 100, 150 and 250- 
watt sizes for use on 220 to 250-volt circuits. 

The gas-filled Mazda C lamps are manufactured in the fol- 
lowing sizes: 75, 100, 150, 200, 300, 400, 500, 750 and 1000 
watts for multiple circuits of 110 to 125 volts; while for 220- 
volt to 250-volt circuits the sizes range from 200 watts to 
1000 watts. Gas-filled lamps for series street-lighting circuits 
are made in sizes giving from 60 candle-power to 1000 candle- 
power and require 5 to 20 amperes. 

330. Efficiency and Life of a Lamp. — The ^' efficiency "of an 
electric lamp is usually expressed in watts per candle (w. p. c), 
which is a ratio of the watts consumed to the mean horizontal 
candle-power produced. If a 50-watt lamp yields an average 
intensity of illumination of 20 candle-power in a horizontal 



478 



LESSONS IN PRACTICAL ELECTRICITY 



direction, its efficiency is 50 -^ 20 = 2.5 watts per candle. The 
lower the numerical value of this efficiency the better is the lamp. 

The amount of light given off by a lamp depends entirely 
upon the temperature at which it is operated. If a lamp is 
operated at a higher voltage than its rating, its temperature 
will be higher and more light will be produced at a lower w.p.c, 
but with a corresponding decrease in the life of the lamp. With 
an increase in temperature the filament will disintegrate more 
rapidly, this being particularly true of the carbon filament. 
The economic or useful life of a lamp ceases long before the 
lamp is " burned out," the term " smashing point " is gen- 
erally used to signify the end of the useful life of a lamp, 
which is reached when the candle-power falls to 80 per cent of 
its original value. 

The following table shows the efficiency and useful life of a 
particular sized 110- volt lamp each of the types having carbon 
and tungsten filaments. 

Table XIX. Efficiencies of Incandescent Lamps 



Type of lamp 


Size lamp 
(watts) 


Efficiency 
(watts per candle) 


Average total life 
(hours) 


Carbon 

Gem 

Mazda B 

Mazda C 


50 

50 

40 

500 


3.1 
2.5 
1.0 
0.7* 


700 

700 

1000 

1000 



* Per spherical candle-power. 

The Mazda C multiple lamps consume about 0.75 w. p. c. 
for the sizes ranging from 100 watts to 500 watts and about 
0.5 w.p.c. for the larger sizes; the large series-type lamps con- 
sume about 0.45 w.'p. c. and have an average life of 1350 hours. 

Incandescent lamps of all kinds give their proper candle-power 
and consume their rated watts only when they are operated at 
the voltage indicated on the label; lamps, however, maybe 
operated, at widely different voltages, with a corresponding 
sacrifice of either life or light. If the voltage on a lamp is 
decreased, the watts and candle-power consequently decrease, 
while the watts per candle and the life are thereby increased, 
and vice versa. In any installation the rated lamp voltage 



ELECTRIC LIGHTING 479 

should be the average, operating voltage of the circuit measured 
at the lamps. Owing to the positive temperature coefficient 
of the Gem and tungsten lamps, they are not as sensitive to 
changes in line voltage as was the carbon lamp ; this is a decided 
advantage on circuits where the voltage fluctuates. 

With the Gem lamp, a 1 per cent increase in voltage increases 
the watts 1.8 per cent, the candle-power 4.4 per cent, and 
decreases the watts per candle 2.4 per cent; if the voltage is 
decreased 1 per cent, the watts decrease approximately 1.8 
per cent, and the candle-power 4.8 per cent, but the watts 
per candle will increase 3 per cent and the life of the lamp about 
18 per cent. With the tungsten lamps a 1 per cent increase 
over the rated voltage increases the candle-power 3.4 per cent 
and decreases the efficiency by 1.6 per cent; it also results in 
about a 14 per cent decrease in the life of the lamp. 

The development of tungsten lamps that can withstand the 
ordinary vibrations and shocks to which lamps are subjected, 
has resulted in their extensive general use, as they produce a 
still whiter light than the Gem lamps and have lower current 
consumption. Their greater efficiency more than balances the 
extra cost of the lamp. A 25-watt tungsten lamp whose effi- 
ciency is 1.25 w. p. c. gives 20 candle-power at one half the 
energy consumption of the 50-watt Gem lamp producing the 
same candle-power. 

The term V' efficiency " as above used in expressing lamp per- 
formance is the ratio of the input in watts to the output in 
candle-power; this is contrary to the usual significance of effi- 
ciency, namely output divided by input. Preference is now 
shown to expressing the output of illuminants in lumens rather 
than candle-power; 1 lumen is emitted by 0.0796 spherical 
candle-power, or 1 spherical candle-power emits 4 tt or 12.57 
lumens. Also, the specific output, stated in lumens per watt, 
is given preference to efficiency expressed in watts per candle. 

To DETERMINE THE SPECIFIC OUTPUT OF A LAMP I 

Multiply the spherical candle-power by 12.57 and divide by 
the power consumption in watts. 

Or -/i X X lumens 12.57 X c. p. ..^,. 

specific output = = — — . . (114). 

watts P 



d80 



LESSONS IN PRACTICAL ELECTRICITY 



Problem 131. — What is the specific output of a 200-watt lamp which 

produces a mean spherical candle-power of 180? 

By Formula (114) 

.^ . , 12.57x180 ,,^, 

specinc output = = 11.3 lumens per watt. 

^00 

331. Light Distribution Curves. — The brightness of a lamp 
is not the same in all directions. For example, a carbon- 
filament lamp may show 16 candle-power in a horizontal direc- 
tion, but only 8 candle-power 
in a direction through the tip 
of the lamp. In order to 
show the intensity of light 
available in any direction it 
is customar}^ to plot a polar 
distribution curve, Fig. 396, 
in which the radial lines rep- 
resent by their lengths the 
candle-powers available in 
the direction in which they 
are drawn. The illustration 
shows the light distribution 
in a vertical plane for a clear- 
glass, 50-watt carbon-fila- 
ment lamp. 

In lighting installations, the lamps are mounted in fixtm-es 
with shades or reflectors, in order to yield the proper intensity 
and uniformity of light where it is desired. Reflectors serve 
primarily to redirect a portion of the light, by means of mirrors 
or by polished aluminum, enamel or mat glass surfaces. Shades 
serve chiefly to conceal the light source so as to avoid glare, 
although they may serve in part as reflectors; they are made 
of translucent glass and many are designed primarily for 
decorative purposes. A number of modern reflectors and 
shades are outlined in Fig. 397 together with their light distri- 
bution curves; the numbers in the columns headed " Light 
Output " show the percentages of light above and below the 
horizontal plane through the lamp. 

332. Incandescent Lamp Circuits. — Incandescent lamps 
are usually operated from low-voltage constant-potential (i.e.. 




Fig. 396. — Vertical Light Distri- 
bution of a Carbon-filament Lamp. 



REFLECTOR 
TYPE 



LIGHT 
OUTPUT 



REFLECTOR 
TYPE 



LIGHT 
OUTPUT 



R.LM.DOME 
Clear Lamp 



PRISMATIC INDUSTRIAL 



7G 



Clear Lamp 



73 



R.L.M. DOME 
Bowl-Frosted Lamp 



LIGHT DENSITY OPAL 



A 



73 



Bowl-Fros-tedLamp 



* 



R.L.M. DOME 

^^ 

Opal Cap 



66 



DENSE OPAL 

A 

Bowl "Frosted Lamp 



20 



60 



ENAMELED BOWL 

A 

Clear Lamp 



65 



DIFFUSING 6L0BE 



With Reflector 



58 



ENAMELED BOWL 



W 



Bowl-Frosted Lamp 



60 



DIFFUSING GLOBE 

O 

Light Opal 



35 



40 



METAL- CAP DIFFUSER 



L 



\ 



Silver Cap 



SHALLOW REFLECTOR 



55 



Diffusing Bowl 



20 



FLAT CONE 



7y 



Clear Lamp 



74 



ONE-PIECE UNIT 



Reflector ^nd Bowl 



55 



FLAT CONE 



Shielding Band 



^ 



65 



SEMI- INDIRECT 
/ f \ 



Light Opal 



60 



MIRRORED GLASS 
Clear Lamp 



SEMI- INDIRECT 



68 



Dense Opal 



INDIRECT 
Clear Lamp 



80 



PORCELAIN ENAMELED 
INVERTED 



Diffusing Glass 
Plate Bottom 



Fig. 397. 



Reflectors and Shades with their Light 
Distribution Curves. 



482 LESSONS IN PRACTICAL ELECTRICITY 

multiple) circuits and supplied by direct or alternating current. 
With a potential of 600 volts, as in street car service, the lamps 
are grouped in multiple-series; for example, five 120-volt lamps 
in series being placed across the mains. For street lighting, a 
constant-current series incandescent lamp system is sometimes 
employed, in which each lamp socket is provided with an auto- 
matic cut-out which short-circuits the filament of the lamp in 
case of failure or burn-out. In the series system the same current 
flows through all the lamps and is maintained constant, con- 
sequently all lamps for such a system should have the same 
current rating. Low-voltage lamps for series burning are 
constructed with filaments of large area to carry the large 
currents. Such lamps with tungsten filaments are made to 
carry currents from 4 to 20 amperes. 

333. Potential Distribution in Multiple-Lamp Circuits. — 
In multiple circuits, the drop on the lead wires is an important 
factor and requires that the lamps be so distributed, and the 
size of the wire so proportioned, that each lamp will receive 
approximately, the same voltage. For example, consider 200 
110-volt incandescent lamps to be connected in parallel at 
various distances along a pair of mains extending 500 feet 
from the generator, and that the P. D. at the geiierator ter- 
minals is 115 volts; the lamps near the generator end of the 
mains will receive a higher voltage than 110 and operate above 
the proper candle-power, while those near the distant end of 
the line will receive less than 110 volts and operate below the 
proper candle-power. To overcome this difficulty, centers of 
distribution are planned in wiring construction, and the lamps 
are grouped so as to be supplied from these centers. Feed 
wires are run from the generator to the points of distribu- 
tion and a constant potential is maintained at these points by 
regulation at the generator. No lamps are connected to the 
feeders. Several sets of mains are run from these centers and 
supply sub-centers of distribution, to which the lead wires 
to the lamps are connected. The total drop or fall in voltage 
from the generator to the lamps in such a feeder-and-main 
system, radiating from a central supply station, may be 5 to 
10 per cent of the generator voltage, so that the generator 
should be operated at a correspondingly higher voltage than 



ELECTRIC LIGHTING 



483 



that required by the lamps. In the wiring of a house for about 
50 110-volt lamps of average size, the drop in voltage, at full 
load, should be about 2 per cent of the pressure supphed at the 
service mains. With an isolated plant in a large office building 
the drop may be 5 per cent of the generator voltage. In a build- 
ing of many floors, a pair of main 
feeders may be run from the gener- 
ator room to, say, every 4 floors; 
each feeder being of such area as 
to supply th€ required current with 
a 5 per cent loss on the line. The 
feeders terminate in cut-outs ar- 
ranged in junction boxes, and sub- 
feeders are carried to each of the 
four floors; these feeders terminate 
at panel-boards. Fig. 398, from 
which smaller branch circuits are 
run to the various lamps on that 
floor. In calculating the size of 
wire for the smaller branch circuits 
a voltage drop of from f to 1 per 
cent is usually allowed. 
In wiring buildings, 
the size of wire is reduced a fuse 
must be inserted, the capacity of 
which must not exceed the permissible current-carrying capacity 
of the smaller wire. Fig. 398 shows a panel-board for distributing 
energy from a three- wire main feeder, to two- wire branch circuits, 
each circuit being supplied with a pair of fuses since these cir- 
cuits are of smaller wire than the main feeder. The panel-board 
shown consists of three vertical copper bus-bars (furnished with 
lugs into which the feeders are soldered) from which branch cir- 
cuits of smaller copper bars are tapped, one wire from the center 
vertical bar and the other from either s de bar, so that the lamps 
receive their proper potential, see ^ 336. The copper bus-bars 
are mounted on slate or marble. Where the energy is distrib- 
uted to lamps with the two-wire main feeders, sub-feeders, etc., 
panel-boards with a two-wire main and two-wire branches are 
used. 




Fig. 398. — Eight-circuit Three- 
wherever wire Main, Two-wire Branch 
Panel or Distributing Board. 

Plug fuses are shown by large circles. 



484 



LESSONS IN PRACTICAL ELECTRICITY 



Most direct- current central stations distribute their electrical 
energy for lighting and power with the three-wire system, Tf 336, 
as it is more economical where the energy is distributed over 
large areas. 

334. Loss on Line Wires. — The weight of copper wire 
required for conducting a certain amount of energy to lamps or 
motors, with the same percentage loss on the transmitting line is 
inversely proportional to the square of the voltage supplied to the 
lamps or motors. For example, suppose 50,000 watts (50 kw.) 
are to be transmitted to some distant center of distribution, 
the permissible loss on the line being 2 per cent or 1000 watts. 
The weight of copper required, when the energy is delivered 
at 100 volts, will be assumed as 1000 pounds; then the com- 
parative weights of copper for other voltages according to the 
above law is given as follows : 



Kw. 


Line volts 


Line 
amperes 


Volts drop 


Loss in 
watts 


Copper 

required in 

pounds 


50 
50 
50 
50 


100 

200 

500 

1000 


500 

250 

100 

50 


2 

4 

10 

20 


1000 
1000 
1000 
1000 


1000 

250 
40 
10 



As the. voltage, at which the above energy is transmitted 
increases, the current to be conducted on the line decreases, 
and the same percentage drop results in a larger voltage drop, 
both influences decreasing the size of the wire, increasing its 
resistance and decreasing its weight. 

In the electrical transmission of power over long distances, 
economy of copper is attained by transmitting the energy at 
a very high voltage and reducing it to a working value at the 
receiving station. Voltages up to 150,000 are used at present 
for transmitting large amounts of power, alternating current 
being used because of the ease of transforming from one voltage 
to another, If 357. 

335. Incandescent Wiring Calculations. — The simplest 
method for calculating the size of wire required to conduct 
current to any given number and size of lamps, with any per- 



ELECTRIC LIGHTING 485 

missible drop in voltage on the line, is to find the resistance of 
the line by Ohm's Law and then consult the wire gage table 
and the table of safe current-carrying capacities, pages 67 and 
306. See also *i 70. 

A general formula to find the area of a wire directly in cir- 
cular mils required to carry any direct current any distance, 
with any given loss on the line, is derived by combining For- 
mulae (10) and (29), which are respectively: 
T3 K X L J TD ^ 

where C. M. = circular mil area, 

K = resistance of 1 mil-foot of wire, 
L = length of circuit in feet, 
I = current in amperes, 
e = volts drop on the line. 

Equating these formulas, there results, 

C.M. = ^.^^^^ . 

e 

Copper being generally used as the conductor, K = 10.79 ^ and 
this formula becomes 

C.M. = Mi^L2li (115). 

e 

To FIND THE SIZE OF COPPER WIRE IN CIRCULAR MILS TO 
CONDUCT ANY GIVEN DIRECT CURRENT A CERTAIN DISTANCE 
WITH A GIVEN DROP ON THE LINE! 

Multiply the total length of the line, in feet, by the resistance 
of a mil-foot of copper wire, namely 10.79, and this product by 
the current, in amperes, to be conducted; divide this product by 
the volts drop on the line. 

The circular mil area so found must be compared with the 
table of current-carrying capacities, page 306. By using a very 
excessive drop on the line the circular mil area calculated by 
Formula (115) in some cases would be much too small for 

^ The size of wire to transmit an alternating current may be approxi- 
mately determined by using the constant 11 instead of 10.79 in Formula 
(115). See note, page 64. 



486 LESSONS IN PRACTICAL ELECTRICITY 

the current to be conducted, hence the necessity of using 
the table of carrying capacities as a check upon the calcular 
tions. Usually the distance from the generator to the center 
of distribution is given and consequently this distance must be 
multiplied by 2 for the two-wire multiple system, to obtain the total 
length of the circuit, L in Formula (115). 

Problem 132. — One hundred and ten 50-watt 110-volt lamps are con- 
nected in parallel and to a center of distribution located 125 feet from the 
generator which develops a P. D. of 113 volts; the potential at the dis- 
tributing center is to be 111 volts. What size wire is required for the 
feeder? 

P 50 

By Formula (55) the current per lamp is I = — = = 0.455 ampere, 

E 110 

and the total current is 110 x 0.455 = 50 amperes. The drop on the line 
ise = 113 - 111 =2 volts. 

By Formula (115) C. M. = 1Q79 X 125 x 2 x 50 ^ ^^^^^^ ^ ^ 

Consulting the table, page 67, the size of wire nearest to 
67,437 C. M. is No. 2 B. & S. with a circular mil area of 66,370, 
which is smaller than that required. It is better to use the 
next larger size of wire, or a No. 1 B. & S., which will give a 
little less drop than 2 volts. Consult the table of safe current- 
carrying capacity, page 306, and it will be found that No. 1 can 
carry 100 amperes, and will thus readily carry 50 amperes. 

A much smaller wire could have been used in this problem, 
as a No. 5, which carries 55 amperes, but the line drop and loss 
would then have been correspondingly larger, since the resis- 
tance of the circuit is increased. The line loss is a constant 
factor — that is, the power, 50 x 2 = 100 watts, lost on the 
line in the above problem is constant, so long as this load is 
constant, and will cost each year a certain sum, while the cost 
of the line installation is only the first cost. The most eco- 
nomical conductor to be installed is that which makes the 
yearly cost of the power lost on the lines equal to the interest 
on the value of the copper invested. 

The volts lost or the drop on any circuit may be measured 
by a voltmeter or may be calculated by Formula (28), when 
the current and resistance of the circuit are known, or derived 
from Formula (115) when the current flowing and the length 
and cross-section of the wire are known. 



ELECTRIC LIGHTING 487 

Problem 133. — An ammeter, connected in series with a circuit of copper 
wire 200 feet long, indicates 25 amperes; the size of wire, measured by a 
wire gage, is No. 10 B. & S. (10,380 C. M.)- What is the drop on the hne? 

By transposing Formula (115) 

10.79 X L X I 10.79 x 200 x 25 _ „ ,^ 

e = — = = 5.2 volts. 

C. M. 10,380 

To FIND THE POWER LOST ON ANY LINE! 

Multiply the volts drop ori the line by the current flowing 
through it, F = e x I, Formula (54). 

Problem 134. — (a) What power is lost on the line in Problem 132? 
(b) What is the cost of this loss for 10 hours per day for 365 days at 10 cents 
per kilowatt-hour? 

By Formula (54) P = e x I = 2 x 50 = 100 watts (a). 

By H 148, the energy lost is 365 x 10 x 100 = 365,000 watt-hours, or 
365 kw.-hours. 

The cost of this energy loss is 365 x 0.10 - $36.50 (b). 

336. The Three- Wire System. — In the three-wire distribu- 
tion system (see T[ 305) two dynamos may be joined in series, 
and the lamps connected between a center or neutral wire, 
joined to the junction 
of the machines, and 
the positive and nega- 
tive wires of the sys- 
tem, as shown in Fig. 
399. When all ten 
lamps illustrated are 
in circuit Fio*. 399 no Fig. 399. — Incandescent Lamps Operated 

, J ^'xi, ' T. in Parallel from the Three- wire System, 

current flows through *" 

the middle wire, and it can be disconnected at the generators 
without affecting the system. If only three lamps are connected 
on the No. 1 side of the system, then current for the two extra 
lamps not paired flows through the middle wire from the -f- 
brush of No. 2 generator. The middle wire is now positive. If 
three lamps are out on the No. 2 side of the system, then current 
for the three lamps on the No. 1 side flows from the + terminal 
of generator No. 1 and returns to it by the middle wire, which is 
now negative. The middle wire, therefore, may have no current 
flowing through it, or current flowing in either one direction or 
the other, depending upon how closely the lamps on both sides of 




488 LESSONS IN PRACTICAL ELECTRICITY 

the system are balanced ; for this reason it is called the neutral 
wire. When all the lamps are turned off on one side of the 
system the neutral wire carries the current for all the lamps 
on the other side. Motors wound for 220 volts are connected 
to the two outside wires and do not, therefore, interfere with 
the balancing of the system. 

The electromotive force is double that of the ordinary two- 
wire multiple sj^stem and the current required for any given load 
is reduced to one half that required on the two-wire system. 
The chief advantage of using the 3-wire system is the saving 
effected in copper, only f of the weight of copper being required 
as compared with the two-wire system. For example, suppose 
1000 pounds of copper are required for a given load operated 
from the 110-volt two-wire system. If the voltage be doubled, 
the weight of copper required will be J as much as before for 
the same percentage loss, % 334, or 250 pounds for the two wires. 
Now since in the three-wire system one extra wire is required, if 
it is made the same size as the others, as is often the case, it 
will weigh J of 250 pounds, or 125 pounds, and the three wires 
will weigh 375 pounds, or only f of the weight of copper required 
by the two-wire system. 

The joint resistance of ten 110-volt, 220-ohm lamps on the 
two-wire system is 22 ohms, Formula (30), while on the three- 
wire system the joint resistance of the same number of lamps, 
two in series, 5 groups in -parallel, is 88 ohms. The joint resis- 
tance of the lamps being four times as great on the three -wire 
system as on the two-wire system, the resistance of the outer 
wires can be four times as great for the same percentage of loss, 
and therefore only one-fourth as large as those required for the 
two-wire system. 

To FIND THE SIZE OF WIRE REQUIRED FOR THE THREE-W^RE 
SYSTEM : 

Find the size of mire required for the same lamp load on the 
two-wire system, hy Formula (115), and divide the number of 
circular mils, so obtained, by 4; or Formula (115) may be modified 
for the three-wire system to read: 

^_j^;^ 10.79xLxI 

4 X e 



ELECTRIC LIGHTING 489 

Problem 135. — The lamps referred to in Problem 132, are to be oper- 
ated from the three-wire system. What size of wire will be required? 

10.79 X L X I 10.79 x 125 x 2 x 50 



By Formula (116) C. M. = 



4 X e 4x2 

16,859 C. M. 



From Table VI, page 67, No. 8 B. & S. has a sectional area 16,510 
C. M. and from Table XIII, page 306, No. 8 will carry 33 amperes. Since 
the current on the three-wire system is one half that for an equivalent 
number of lamps on the two-wire system, the wire in this problem will 
only carry | of 50, or 25 amperes, and the No. 8 wire is therefore sufficiently 
large. The neutral wire may be made the same size as the outside wires; 
sometimes it is made one half as large since it is hardly probable that 
all the lamps on one side of a well-balanced three-wire system will be out 
and the others all burning. A further saving of copper is then attained. 

337. Motor Wiring Calculations. — To find the current 

REQUIRED BY A MOTOR WHEN THE OUTPUT, EFFICIENCY, AND 
VOLTAGE ARE KNOWN! 

If the output of the motor is expressed in kilowatts (kw.), 
multiply the kw. rating by 1000 and divide by the voltage of the 
motor and by its efficiency, Formula (117). If the output is ex- 
pressed in horse power, multiply the H. P. by 746 and divide this 
product by the voltage of the motor and by its efficiency, Formula 
(118). 

. kw. X 1000 



E X %M 



(117). 



^ H. P. X 746 

where E = voltage required by the motor, 
kw = kilowatt rating of the motor, 
H. P. = horse power of the motor, 
% M = efficiency of the motor, expressed as a decimal. 

To FIND THE SIZE OF WIRE, IN CM., NECESSARY TO TRANS- 
MIT ENERGY TO A MOTOR OVER ANY DISTANCE, WHEN THE VOLT- 
AGE AND EFFICIENCY OF THE MOTOR ARE KNOWN: 

Determine the current required by the motor from Formula 
(117) or (118) and then use Formula (115). Or the procedure 
may be stated as follows: 



490 LESSONS IN PRACTICAL ELECTRICITY 

Multiply the rated horse power of the motor by 746, then by 
the length of the circuit in feet and then by 10.79; divide this 
result by the product of the voltage required by the motor, the 
drop on the line and the efficiency of the motor, Formula (119). 
Average motor efficiencies follow: 

IH. P 70 per cent 

3H. P 75 '' " 

5H. P 80 " " 

10 H. P ....85 " " 

50 H. P 90 " "i 

Letting e be the voltage drop there results from combining 
Formula (115) with Formula (118), 

C.M.= H.P.X746XLX10.79 

E X e X % M ^ ^ 

Problem 136. = What size of wire is required to conduct current to a 
220--volt 5-H. P. motor located 150 feet from the meter; the drop on 
the line is to be 5 volts and'the efficiency of the motor is 80 %? What cur- 
rent does the motor take? 

TD TT 1 M1o^ T H. P. x746 5 x746 ^, 

By Formula (118) 1 = —- —- = --— =21 amperes. 

^ E X % M 220 X 0.80 ^ 

By Formula (119) 

H. P. x746xLxl0.79 ^ 5 x 746 x 150 x 2 x 10.79 
■ ■ " E X e X % M 220 X 5 X 0.80 

= 13,720 C. M. 
From Table VI, page 67, No. 8 B. & S. has a sectional area 16,510 C. M. 
The motor requires 21 amperes, and from Table XIII, page 306, the carry- 
ing capacity is 33 amperes; therefore No. 8 is the proper size of wire. 

To FIND THE HORSE POWER DEVELOPED BY A MOTOR: 

Multiply the pressure applied to the motor terminals by the 
current supplied to it and by the efficiency of the motor; divide 
this result by 746. 

Problem 137. — A current of 45 amperes is supplied to a motor, having 
an efficiency of 85 per cent, under a pressure of 220 volts. What horse 
power is developed by the motor? 

„ „ I X E X % M 45 X 220 X 0.85 ,, ^ ^ 

tx. r. = = = il xl. r^. 

746 746 

338. Installation of Interior Wiring. — All interior wirmg 
must be installed in such a manner, that it will be protected from 
mechanical injury, and be safe as regards fire hazard or danger 



ELECTRIC LIGHTING 491 

to life; therefore wherever wires are installed in buildings the 
method of installation must conform to the rules of the National 
Board of Fire Underwriters as set forth in its '' National Elec- 
trical Code." This Code is in effect throughout the United 
States and Canada, and gives definite rules for the installation 
of all kinds of wiring. It also specifies carefully the kind of 
material, such as wire, conduit, fuses, etc., that may be installed. 
Copies of the code will be found useful for reference and may 
be obtained by applying to any of the Fire Underwriters' 
offices. 

Installation of wiring for light or power service, at voltages 
not exceeding 500 volts, may be done by any one of the follow- 
ing plans, all of which are approved by the code, but the use of 
some of them is restricted to special places: 

Oyen or Exposed Wiring. — Wires are supported on porcelain 
knobs or cleats; the knobs or cleats should separate the wires 
about 2J inches and should be | inch from the surface along 
which they run. 

Concealed, Knoh and Tube. — Wires are concealed between 
floor beams and studs of a building, knobs being used to sup- 
port whes when run parallel to beams or studs and porcelain 
tubes when run at right angles through the beams or studs. 

Molding Work — Wires are run in a wood or metal molding. 
The metal molding consists of a sheet steel trough or backing 
and a steel cover which is snapped on the backing after wires 
are in place. Wood molding consists of a backing with grooves 
for the wires and a capping which is nailed to the backing after 
the wires are in place; this molding is made for two wires and 
for th^ee wires. Molding work is particularly adapted to the 
wiring of buildings after their completion and has the advan- 
tage of cheapness, simplicity and accessibility. 

Rigid Conduit. — Wires are run in unlined conduits which 
are free from scale on the inside and are coated with enamel 
inside and outside; the outside is sometimes galvanized when 
used where the pipe is exposed to the weather. Conduits must 
be continuous from outlet to outlet, at which places metal 
junction boxes made for the purpose are located; the conduit 
must properly enter and be secured to all fittings, and the 
system must be mechanically strong. Conduit affords the best 



492 LESSONS IN PRACTICAL ELECTRICITY 

protection to the wires from mechanical injury and may be used 
for all classes of service. It is chiefly used in buildings of fire- 
proof construction where wires are concealed; it is also fre- 
quently used for circuits run exposed in power houses and indus- 
trial establishments. Conduit systems must be grounded, that 
is connected to the earth, by connecting the conduit to a water 
pipe (on the street side of the meter); grounding is necessary 
so that in case of a breakdown of the wire insulation, the con- 
duit will not be charged to a dangerous potential. 

Flexible Conduit. — Wires are installed in a flexible conduit that 
is made of steel strips wound spirally, to form a tube; the edges 
of the strip interlock in such a manner that the tube can be 
bent to a small radius. Flexible conduit is generally used in 
concealed work where rigid conduit could not be used. It is 
not water-tight and therefore is not as suitable as the rigid con- 
duit where exposed to moisture. 

Armored Cable. — A flexible armor similar to the above 
flexible conduit is placed directly upon the wire. The wire is 
rubber insulated and covered with a braid the same as the wire 
used in metal conduit systems. This armored cable is made 
with either single, double or triple conductors and is used for 
the same classes of service as flexible conduit, in fact it is used 
more frequently than the flexible conduit as it is cheaper and 
easier to install. 

QUESTIONS 

1. What is the distinction between an arc and an incandescent lamp? 

2. What is the relative consumption of carbon in a lamp used, (a) 
on direct-current circuits; (6) on alternating-current circuits? 

3. From what part of the arc is the most light emitted and what 
is the general direction of maximum intensity? 

4. Describe the principle of action in a differential arc lamp. 

5. What is the difference between an enclosed and an open air arc? 
State two advantages of the former. 

6. Why are lamps used for street lighting generally operated in series? 

7. Describe the mercury-vapor lamp. 

8. What are the advantages of the tungsten filament lamp over the 
carbon lamp? 

9. Describe several methods used in the wiring of houses. 

10. What is the advantage of the three-wire distribution system over 
the two-wire system. 



ELECTRIC LIGHTING 493 

11. How are incandescent lamps rated as to size and efficiency? 

12. Sketch the light distribution curve of a semi-indirect lighting 
fixture. 



PROBLEMS 

1. A 110-volt, 20-c. p. carbon lamp requires 50 watts. Give the fol- 
lowing: (a) efficiency of lamp; (6) lamps per H. P.; (c) cost of operating 
the lamp for 100 hours if the energy costs 10 cents per kw.-hour; (d) specific 
output. Ans. (a) 2.5 w. p. c; (6) 15 lamps; (c) $0.50; (d) 5.03 lumens 
per watt. 

2. A 25- watt Mazda lamp has an efficiency of 1.25 watts per candle. 
Give the following: (a) candle-power produced; (6) lamps per H. P.; 
(c) cost of operating this lamp for 100 hours, if the energy costs 10 cents 
per kw. hour? Ans. (a) 20 c. p.; (b) 29 lamps; (c) $0.25. 

3. Two hundred 50- watt 110-volt lamps are connected in parallel 
and are fed from a center of distribution located 100 feet from the generator. 
What size of wire will be required, if 2^ volts are to be lost on the main 
feeders? Ans. No. 1 B. & S. 

4. If 25-watt Mazda lamps were used in Problem 3, what size wire 
would be required, allowing 2 volts loss on the line? Ans. No. 3 B. & S. 

5. A series arc circuit, 5 miles in length, is constructed of No. 6 
B. & S. wire and carries 10 amperes, (a) What is the voltage drop on 
the line? (6) What power is lost on the line? (c) What is the yearly cost 
of the power lost on the line, operating 10 hours a day for 365 days at 
5 cents per kw.-hour? Ans. (a) 108.5 volts; (6) 1085 watts; (c) $198. 

6. The lamps in Problem 3 are to be supplied from a three- wire 
multiple System. What size wire will be required? Ans. No. 5 B. &. S. 
(when checked by Table XIII). 

7. With 6 volts drop on the line what size wire is required to carry 
current for a 10-H. P. 220- volt motor, located 150 feet from the source of 
supply; efficiency 85 %? Ans. No. 7 B. & S. 

8. What current will the motor in Problem 7 receive? Ans. 39 amperes. 

9. A 30-ampere 30-volt motion-picture Mazda C lamp has a specific 
output of 27.4 lumensper watt, (a) Determine its spherical candle-power. 
(6) Calculate the watts per spherical candle-power. Ans. (a) 1962 c. p.; 
(&) 0.46. 



LESSON XXVIII 
ALTERNATING CURRENTS 

Principles of Alternating Currents — Theory of Alternating Currents 

— Sine Curves — Frequency, Alternations and Cycles — Inductance 

— Reactance — Impedance — Graphical Illustrations of Impedance, 
Reactance and Resistance — Capacity — Peculiarities due to In- 
ductance and Capacity — Impedance of Circuits having Inductance, 
Capacity and Resistance — Ohm's Law for Alternating-Current Cir- 
cuits — Impedances in Series — Impedances in Parallel — Effective 
Values of Alternating Currents and E. M. F.'s. — Components of 
Impressed E. M. F. — Angle of Lag or Lead, and Phase — Deter- 
mination of Power Expended in Alternating-Current Circuits — 
Questions and Problems. 

339. Principles of Alternating Currents. — A continuous or 
direct current is one which always flows in one direction, while 
an alternating current is one which continually changes both 
its strength and direction. The various principles and facts 
concerning direct-current distribution which have been explained 
in the preceding lessons apply in general also to alternating- 
current systems. But in addition to the simple reactions, 
which occur with direct currents, there are certain other factors 
that must be considered in connection with alternating-current 
transmission. 

The flow of a direct current for a given impressed E. M. F. 
is entirely determined by the ohmic resistance of the various 
parts of the circuit. The flow of an alternating current depends 
not only upon the resistance, but also upon any inductance 
(self or mutual) or capacity that may be contained in or con- 
nected with the circuit. These two factors, inductance and 
capacity, have no effect upon a direct current after a steady 
flow has been established, which condition usually requires 
only a fraction of a second. In an alternating-current circuit 
either or both of them may be far more important than the 
resistance and in some cases may entirely control the action 
of the current. Alternating-current problems involving the 

494 



ALTERNATING CURRENTS 



495 



consideration of these three factors are usually more complicated 
and difficult to solve than those relating to direct currents. 
The reason for employing alternating currents for electric 
lighting and power purposes is the economy effected in 
the cost of transmission which is accomplished by the use 
of high voltages and transformers. It has already been shown, 
^ 334, that the cross-section of a wire necessary to convey a 
given amount of electrical energy in watts with a certain per- 
centage drop of potential, is inversely proportional to the square 
of the voltage supplied ; for example, it requires a wire of only 



One Cycfe- 

— One Period - 




Fig. 400. — Plotting a Sine Curve. 

one quarter the cross-section and weight if the initial voltage 
is doubled. The great advantage thus obtained by the use of 
high voltages can be realized either by a saving in the weight 
of wire required or by transmitting the energy to a greater 
distance with the same weight of copper. 

340. Theory of Alternating Currents. — Under the theory 
of dynamos it was explained that each armature coil of a gen- 
erator produces an E. M. F. which rises from zero to a certain 
maximum value and falls to zero again, then reverses in direc- 
tion, rising to a maximum value and returning to zero, W 277, 
278. Referring to Fig. 400, suppose that the line OP revolves 
at a uniform rate about the point 0, that is, one end remains 
fixed at O while the point P moves around the circle in an 
anti-clockwise direction. The angle A between OP and the 
horizontal line Oa will then be constantly changing. When 
point P is at a, that is, when the point P is just starting on a 
revolution, the angle A is zero, because OP lies along Oa. When 



496 LESSONS IN PRACTICAL ELECTRICITY 

P reaches f , angle A has become 90° ; when it reaches k, 180° ; 
p, 270°; and a again, 360°; or in other words P has reached 
the starting point again, having made a complete revolution. 
Now let us imagine the point P to be an armature coil revolving 
between the poles NS. By following the curve we note that 
as the coil, or the point P, moves from a to f the induced E. M. F. 
gradually rises from zero at a to its maximum value at f in the 
circle since the coil when 90° from a is in the position of maxi- 
mum induced E. M. F.; then moving from f to k the E. M. F. 
gradually falls to zero at k; continuing the revolution of the 
coil we find (observing the curve) that the E. M. F. gradually 
rises from zero at k to its maximum value at p (270°), but in 
the opposite direction, since the coil is now under the opposite 
or S pole. Thereafter the induced E. M. F. again falls to 
zero as the point P travels from p to a (360°). 

The variation of an alternating current may always be repre- 
sented by a wave-like curve as shown in Figs. 315 and 400. 
In order to study the effects of an alternating current it is 
necessary to know the law according to which this curve 
varies. A consideration of the manner in which the curve 
in Fig. 400 has been formed will show that the ordinate of 
any point P is proportional to the sine of the angle A for that 
point. Hence it is called a sinusoid or a sine curve. 

The ideal pressure curve from an alternator is sinusoidal. 
Commercial alternators, however, do not generate true sinu- 
soidal pressures, but they so closely resemble the curve depicted 
in Fig. 400 that for most purposes the sine curve can be applied 
with propriety. 

341. Sine Curves. — The sine curve or curve of E. M. F. 
is plotted along a horizontal line, such as that marked Time 
in Fig. 400, as follows: Divide some convenient length along 
this hne, such as BC, into say 20 parts, and also divide the cir- 
cumference along which P moves into 20 parts. We then have a 
straight line with subdivisions representing the distances moved 
by P around the circle or, what is the same thing, the angles 
made by the radius with its first position in its revolution 
around the center O; and these divisions may also be taken 
to represent the time it takes P to turn through the various 
values of the angle A. Suppose P to have made 2V of a revo- 



ALTERNATING CURRENTS 497 

lution and to have reached the point b, take a distance along 
the time base equal to 2V of the length BC from to 1, and at 
the latter point erect a perpendicular; where this cuts a hori- 
zontal line drawn through point b on the circle will give one 
point on the curve. In the same way for position c we erect a 
perpendicular at the end of the second space along the time 
axis, marked 2, and where this perpendicular cuts a horizontal 
line drawn through c on the circle, yields the second point on 
our curve. This operation is repeated for different positions 
of P around its circular path, a series of points being obtained, 
which, when connected, are found to he on a wavy line called 
the sine curve. 

The wave is known in trigonometry as a sine wave for the 
following reason: Draw the perpendiculars PR and PY to the 
horizontal and vertical axes respectively. The ratio of PR to 
OP is known as the sine of the angle A; OP remains constant 
while PR increases and decreases as P revolves around the center 
O. The line PR is therefore always proportional to the sine of 
the angle A, and the perpendicular line, or ordinate, that deter- 
mines the height of the wave curve at any point is equal to the 
value of the ordinate or perpendicular PR corresponding to 
that point. The wave, therefore, at any point, has a height 
which is proportional to the sine of the angle that corresponds 
to that point, hence the name sine wave. 

342. Frequency — Alternations — Cycles. — When, as stated 
above, the alternating current or E. M. F. has-passed from zero, 
to its maximum value in one direction, to zero, then to its 
maximum value in the other direction, and back to zero, the 
complete set of values passed through during that time is 
called a cycle. This cycle of changes, which is represented 
by the sine curve depicted in Fig. 400, takes place in a certain 
time, called a period; and since the cycle is repeated indefi- 
nitely at each revolution of the armature the currents pro- 
duced by such an E. M. F. are called periodic currents. The 
number of complete periods in one second is called the frequency 
of the pressure or current. In Fig. 400 a period is represented 
by the time elapsing from one positive maximum to the next 
positive maximum, although it makes no difference whether 
one considers a period or cycle to begin when the E. M. F. 



498 LESSONS IN PRACTICAL ELECTRICITY 

curve is at the horizontal or zero Hne, or when it has its maxi- 
mum value, or at any other point; a cycle or period comprises 
the succession of changes which occur from any one point on 
the curve to the next point where the curve indicates the same 
character of E. M. F. or current. The time elapsing from 0° 
to 360°, Fig. 400, would constitute a period, since a period 
represents the time of one complete cycle of events. 

The term frequency is applied to the number of cycles com- 
pleted in a unit of time — one second. It is expressed in 
cycles, meaning cycles per second. The word alternations was 
formerly used to express the frequency of an alternator, mean- 
ing the number of alternations per minute. An alternation is 
half a period or cycle. In Fig. 400, from 0° to 180° is one 
alternation; since the current changes its direction at each half 
cycle, it follows that the number of alternations or of reversals 
is twice the number of cycles in a given time. 

If the current from an alternator performs the cycle of 
events depicted in Fig. 400 from B to C sixty times a second, 
it is said to have Si frequency of 60 cycles;, this would mean 120 
alternations per second, or 120 X 60 = 7200 alternations per 
minute. 

The frequency of an alternating current is always that of 
the E. M. F. producing it. 

To FIND THE FREQUENCY IN CYCLES OF THE PRESSURE OR 
CURRENT OF ANY. ALTERNATING-CURRENT GENERATOR: 

Multiply the number of pairs of poles by the speed of the arma- 
ture in revolutions per second. 

Let f = frequency (cycles per second), 
P = number of pairs of poles, 
N = speed (revolutions per minute). 

Then i=Fx^ (120). 

60 

Problem 138. — (a) What would be the frequency (in cycles) of the 
current furnished by an alternator having 10 poles and running at 720 
revolutions per minute? 

By Formula (120) f=Px^ =^x^ = 5xl2=60 cycles. 
60 2 60 



ALTERNATING CURRENTS 499 

The frequencies of commercial alternating currents depend 
upon the nature of the services required. For power use a low 
frequency is desirable, frequencies for this purpose varying 
from 60 down to 25. For lighting, frequencies from 40 to 60 
are in general use; formerly they ranged up to 125 cycles. 
Very low frequencies cannot be used for lighting owing to the 
flickering of the lamps. A large number of central stations 
have adopted a frequency of 60 as a standard for lighting and 
for power transmission. 

343. Inductance. — Most of the pecuHarities that alternat- 
ing current exhibits, as compared with direct current, are due 
to the fact that an alternating current is constantly changing 
in direction, whereas a continuous current flows uniformly in 
one direction. As has been shown in previous lessons, when a 
current flows through a wire it sets up a magnetic field around 
the wire, and in consequence with an alternating current this 
magnetic field will also change continually. Whenever the 
magnetic field surrounding a wire is made to change, an E. M. F. 
is set up in the wire, and this induced E. M. F. opposes the 
current. For example, when the current rises in the positive 
direction, the lines of force increase in, say, the clockwise 
direction about the conductor; after the current passes the 
maximum value and begins to decrease, the lines of force 
commence to collapse, reaching zero value when the current 
reaches zero; then when the current rises in the negative 
direction the magnetic lines expand in the counter-clockwise 
direction and so on. The result is that the counter E. M. F. 
of self-induction, instead of being momentary (as when a direct 
current is established and interrupted through a conductor) is 
continuous, but varies in value like the applied E. M. F. or the 
current. 

The value of an induced E. M. F. is proportional to the 
rapidity with which lines of force are cut by the conductor, and 
as the lines of force vary most rapidly when the curve of current 
or magnetic flux passes the zero point (changing from + to -) 
or vice versa, the induced E. M. F. is a maximum at that 
moment. When the current, and therefore the magnetism, is 
at the maximum value in either direction, its strength varies 
very little within a given momentary period of time, and 



500 



LESSONS IN PRACTICAL ELECTRICITY 




consequently the induced E. M. F. is zero at the moment the 
current and magnetism are at maximum value. Therefore 
the E. M. F. of self-induction does not rise and fall in unison 
with the applied E. M. F. and the current, but lags behind the 
current exactly a quarter of a cycle, as shown in Fig. 401. 

This property of a wire or coil to act upon itself inductively 
(self-induction) or of one circuit to act inductively on another 

independent circuit (mutual 
induction) is termed induc- 
tance. The unit or coefficient 
of inductance is called the 
henry, the symbol for which 
is L, % 258. The amount of 
inductance possessed by a 
rig.40L-EMT of&^lf-induction • ^^ depends upon the 
Lagging a Quarter of a Cycle behind ^ . '^ 

the Current. amount 01 magnetic flux as- 

sociated with it. Most elec- 
trical devices have inductance; a coil of wire may have a high 
inductance, a lamp filament has very little. 

344. Reactance. — From ^^ 258, 259 and 343 we learn that 
the effect of inductance in an alternating-current circuit is to 
oppose the flow of current on account of the counter E. M. F. 
which is set up. This opposition may be considered as an 
apparent additional resistance, and is called inductive reactance 
to distinguish it from ohmic resistance. 

Reactance is expressed in ohms, like resistance, because it 
constitutes an opposition to the flow of the current. Unlike 
resistance, however, this opposition does not entail any loss 
of energy because it is due to a counter pressure and is not 
a property analogous to friction. Its effect in practice is to 
make it necessary to apply a higher E. M. F. to a circuit in 
order to pass a given current through it than would be required 
if only the resistance of the circuit opposed the current. The 
value of the reactance in ohms due to inductance may be ex- 
pressed by the formula 

Xi = 27r X f X L, (121). 

where L = inductance (henrys), 

f = frequency (cycles per second), 
TT = 3.1416. 



ALTERNATING CURRENTS 501 

Transposing Formula (121) we have 

. 1 ^ reactance ^ Xz /^««x 

inductance = — , or L = .... (122). 

27r cycles 27rf 

Problem 139. — What would be the reactance of a coil of wire having 
an inductance of 0.02 henry when connected to an E. M. F. of 60 cyles? 
By Formula (121) X^ = 27r x f X L = 6.28 x 60 x 0.02 = 7.536 ohms. 

Problem 140. — What would be the inductance of a coil which has 
a reactance of 8 ohms when connected to an E. M. F. of 120 cycles? 

By Formula (122) L = |i - ^^^^ - ^-|^ = 0.0106 her>ry. 

345. Impedance. — The circuits met with in practice always 
have resistance as well as inductance. The combined effect 
of resistance and reactance is called impedance to distinguish 
it from the other two, and its symbol is Z. The impedance in 
ohms of any circuit may be expressed by the following formulae : 

Impedance = Vresistance^ + reactance^, 

or Z = VR2 + (27rfL)2, (123). 

or Z = VWyX] (124). 

Problem 141. — What would be the impedance of a coil of 4 ohms 
resistance and 8 ohms reactance? 



By Formula (124) Z = VR2 + X| - V42 + 82= VI6 + 64 = 8.94 ohms. 

Given the impedance and resistance, to find the re- 
actance, use: 

Xi = VZ2 - R2 . (125). 

Given the impedance and reactance, to find resis- 
tance, use: 



R = VZ2 - X] (126). 

346. Graphical Illustrations of Impedance, Reactance and 
Resistance. — The relations expressed by Formula (123) may 
be represented by a right-angled triangle, ABC, Fig. 402 (a). 
The true ohmic resistance R is laid off on a convenient scale 
to form the base line, the reactance 27rfL or X; is laid off also 
in ohms to form the perpendicular, and the impedance in ohms 
is found by measuring the hypotenuse of the triangle, since 
it is equal to the square root of the sum of the squares of the 



502 



LESSONS IN PRACTICAL ELECTRICITY 





// 



other two sides. This is merely a mathematical coincidence, 
however, resulting from the use of the sine curve as the basis 
of alternating-current calculations. Such 
a triangle is frequently used to represent 
the relations between resistance, reac- 
tance and impedance and also for con- 
venience in obtaining other quantities. 

When the reactance is small compared 
with the resistance, it has very little effect. 
This is shown in Fig. 402 (b) . The Hne BC 
is short compared with AB and the im- 
pedance represented by AC is not much 
larger than the resistance AB. When the 
reactance is doubled, or BC = 2 x BC, 
the impedance AC is not much increased 
over its former value AC. When the 
reactance is large compared with the re- 
sistance, the impedance , is much greater 
than the resistance. This is shown in 
Fig. 402 (c). 

In coils where the inductance is large 
compared with the resistance, the resis- 
tance may often be entirely neglected, and 
we may say that the current equals the 
E. M. F. divided by the reactance. If the 
frequency is doubled in such cases, the 
reactance is doubled and the current at 
the same potential is reduced one-half. 
347. Capacity. — Capacity is the third quantity which affects 
the flow of an alternating current and which, like inductance, 
does not enter into the consideration of the steady flow of 
direct current. 

If we take a number of sheets of tin-foil, interleave them with 
a corresponding number of slightly larger sheets of waxed 
paper, connect alternate tin-foil sheets together and then 
press the whole mass tightly together, we have an electrical 
condenser, If 264. The construction of a condenser is shown in 
Figs. 285 and 286. If a galvanometer were connected in circuit 
with a condenser and a direct E. M. F. applied, it would be 



/ 



I i^ 



/?es/sta/7ce 



Fig. 402. — Graphical 
Representation of Impe- 
dance, Reactance and 
Resistance. 



ALTERNATING CURRENTS 503 

noticed that just after the pressure was applied a current 
would flow for a short interval; also that if the terminals were 
disconnected from the source of current and connected together, 
the galvanometer would be deflected momentarily in the reverse 
direction. There is a momentary current just at the instant 
the condenser is charged, and a reverse momentary current 
when it is discharged. 

A condenser is said to possess electrostatic capacity for stor- 
ing a quantity of electricity, the capacity being measured in 
terms of the farad as a unit. The farad is the capacity of a 
condenser which will contain one coulomb of charge when its 
plates have a difference of potential of one volt. Since this 
unit is much too large for ordinary use a smaller unit, the 
microfarad, or millionth part of a farad, is generally used. 

If a condenser be connected to a source of alternating cur- 
rent and a galvanometer connected in the circuit, it will be 
found that the galvanometer indicates a current as long as 
the alternating E. M. F. is applied to the circuit. The cir- 
cuit acts just as if it were complete, and we have the peculiar 
effect of a current apparently flowing through a circuit which 
has a complete break in it, for it will be remembered that 
there is no connection between adjacent plates of the con- 
denser. 

What actually occurs is that the condenser is charged to 
a potential equal to the maximum applied E. M. F. during 
the first quarter of a cycle, is discharged during the second 
quarter, is charged again, but in the opposite direction, during 
the third quarter of the cycle, and is discharged during the 
fourth quarter, this process continuing as long as the condenser 
remains in circuit and the alternating current continues to 
flow. The condenser is thus charged and discharged continu- 
ously, so that current will flow in the circuit in spite of the fact 
that the two sides of the condenser are insulated from each 
other. Thus we see that a condenser in an alternating-current 
circuit is equivalent to a closed circuit having a certain ap- 
parent resistance in ohms which is called its reactance, analogous 
to that due to inductance. The flow of current increases directly 
with the capacity and with the frequency, therefore the reac- 
tance is inversely proportional to these quantities. Calhng C 



504 LESSONS IN PRACTICAL ELECTRICITY 

the capacity in farads, the reactance in ohms due to the con- 
denser is: 

^-2^ •■■'••• -(127). 

Problem 142. — What would be the reactance of a 25-microfarad con- 
denser to an alternating current of 60 cycles? 

Since 25 microfarads = 0.000025 farad, by Formula (127) 

'^" ^ MC ^ 2 X 3.1416 X 60 X 0.000025 ^ 0.0094 ^ ^^^'^^ ^^^"^s- 

Most circuits possess to a greater or less degree the same 
property as a condenser, namely that of holding a certain 
charge or quantity of electricity, and this has a marked influ- 
ence upon the behavior of an alternating current flowing in 
the circuit. The capacity of most circuits met with in prac- 
tice is quite small in comparison with their inductance and 
resistance, consequently its effect is riot usually so noticeable; 
however in some cases, especially in underground cables and long 
overhead lines, these effects become important. Ordinary (elec- 
trical devices, such as lamps, motors, etc., have little electrostatic 
capacity. 

348. Peculiarities Due to Inductance and Capacity. — The 
following experiments illustrate cases where alternating cur- 
rents differ in their behavior from direct currents. These 
effects are due to the fact that the current is continually 

changing and that either inductance 

or capacity is present in the circuit. 

The student is advised to read again 

11260. 




Experiment 106. — Connect an incandes- 
cent lamp, L, Fig. 403, in series with a coil, 
*| f ' M, which has a considerable amount of in- 

llOVolfs ductance. Connect the two across a 110-volt 

p- ^Q3 Effect of alternating-current circuit. Measure the 

Inductance in an Alter- voltage across the lamp, Ei, and that across 
nating-current Circuit. the coil, E2, add these two voltages, and you 

will obtain the apparently impossible result 
that the arithmetical sum is greater than the line voltage, E. Now if these 
two devices are connected across a direct- current circuit and the drop 
across the lamp is added to that across the coil the sum of the two would, 
of course, be equal to the line voltage, 110 volts. (See ^ 351.) 



ALTERNATING CURRENTS 



505 



Experiment 107. — If we place a condenser, C, Fig. 404, in series with a 
lamp, L, and apply a direct current to the terminals, Ti and T2, no steady 
current will flow -unless the insulation of the condenser breaks down. 
It will be noticed that just after the pressure 
is applied a current would flow for a short in- 
terval and cause the lamp to flash; also if the 
terminals, Ti and T2, are disconnected from the 
source of the current and connected together, 
the lamp will flash again, there being a mo- 
mentary current at the instant the condenser 
is charged and a reverse momentary current 
when it is discharged. If we now apply an 
alternating pressure of 110 volts to the termi- 
nals the lamp will be steadily illuminated, for 
when -the current flows in one direction the con- 
denser is charged, and when the current re- 







r^'- 






■ ^ 






T2 




T, 



110 Volts 



Fig. 404. —Effect of 
Capacity in an Alter- 
nating-current Circuit. 

verses the condenser is discharged through the lamp, the action taking 
place so rapidly that the lamp is illuminated as if connected directly to the 
alternating pressure. 

Experiment 108. — Fig. 405 shows an arrangement that illustrates a 
peculiar effect of inductance and capacity combined. Here Li, L2 and L3 
are incandescent lamps of the same kind, M is an adjustable inductance 

made up of a coil that can be 
L I • \^ ' \ ' \ 1 moved over an iron core, and C is 

a condenser. M and C are each in 
series with a lamp, and are each 
in one of two branch circuits into 
which the main circuit is split. If 
this combination is connected to a 
direct- current circuit of, say, 110 
volts no current at all would flow 
through the lower branch on ac- 
count of the condenser. If, how- 
ever, alternating'current is applied, 
current will flow through each 
branch. The striking point is that 
if M is adjusted to the proper 
amount, lamp Li can be made to operate at a dull red while lamps L2 and 
L3 are illuminated to full brightness. In other words, the sum of the two 
currents through L2 and L3 is less than either current singly, and the cur- 
rent flowing in the main circuit is less than the current flowing in either 
of the branch circuits. Such a result would, of course, be impossible with 
direct currents. (See ^ 352.) 

349. Impedance of Circuits having Inductance, Capacity 
and Resistance. — When a circuit contains both inductance and 
capacity, the net reactance, X, is equal to the arithmetical 




Fig. 405. — The Combined Effect of 
Inductance and Capacity in an Alter- 
nating-current Circuit. 

The inductance M may be adjusted so that 
the value of the current in the main circuit 
will be less than the current in either branch 
circuit. 



506 LESSONS IN PRACTICAL ELECTRICITY 

difference between the inductive reactance, X^, and the capacity 
reactance, Xc, or X = X^ - Xc. 

Therefore the impedance of a circuit containing inductance, 
capacity and resistance is equal to 

Vresistance ^ + (inductive reactance - capacity reactance) ^ 

or Z = VW+X' = Vm + (Xi - XcY .... (128). 

Problem 143. — What would be the combined impedance of a circuit, 
having a coil of 4 ohms resistance and of 0.01 henry inductance in series 
with a condenser of 25 microfarads capacity, to an alternating current of 
120 cycles? 

By Formula (121) Xi = 27rfL = 6.28 X 120 X 0.01 = 7.53 ohms. 

By Formula (127) 

Xc = -^ = ^ = 53.07 ohms. 

27rfC 6.28 x 120 x 0.000025 

By Formula (128) Z = Vr^+ (X, - X,)^ = V42 + (7.53 - 53.07)^ 
= V16 4-2073 = 45.71 ohms. 

The foregoing may be made clearer by the use of the tri- 
angular diagram shown in Fig. 406, which shows the relation 
between capacity reactance, resistance and impedance. It will 

be observed that the line repre- 
^psfsfance, J? scutiug Capacity reactance proj ects 

downward from the horizontal line, 
while the inductive reactance line 
(Fig. 402) projects upward; this 
indicates the opposite properties 
of inductance and capacity as re- 
Fig. 406. — Diagram show- gards their effect on the E.M.F. 
ing the Relation between Capa- and current in the circuit. When 
Impedfnce!''''^' ^^'^'^^'"'^ ^""^ a circuit contains both inductance 

and capacity the difference between 
the lengths of the lines representing inductive and capacity 
reactances will represent the resultant or net reactance X, of the 
circuit, as shown in Fig. 407. In the figure the capacity reac- 
tance, Xc, is one third as great as the inductive reactance, Xi; 
the resultant or net reactance, X, therefore, is two thirds as 
great as the inductive reactance, and the impedance line is 
drawn from the left-hand end of the base line to a point two 
thirds up along the line representing inductive reactance. The 




ALTERNATING CURRENTS 



507 




J'es/sfance./? 



Fig. 407. — Resultant Re- 
actance and Impedance of a 
Circuit Containing Inductance 
and Capacity. 



dotted line, a, shows what the impedance would be if there 
were no capacity in the circuit, and the dotted line, b, shows 
what the impedance would be if 
the inductance were not present. 

It is obvious that when X^ and X^ 
are equal, the difference between 
them is zero, making the impedance, 
Z, equal to Vr^, which of course 
is R. When this is the case the cir- 
cuit operates as though there were 
neither inductance nor capacity 
present, the current rising and falling 
in unison with the E. M. F. Re- 
ferring to Fig. 407, if the lines Xz and X^ were of equal length 
their difference would be zero, and the impedance line would 
be identical with the resistance line. Such a circuit is said to 
be in resonance with the impressed alternating E. M. F. 

350. Ohm*s Law for Alternating-Current Circuits. — In 
dealing with direct-current systems the relation existing between 
the pressure, current strength and resistance is fully explained 
by Ohm's Law, i.e., I = E ^ R. This law, however, cannot be 
applied in the same form to alternating-current circuits, since 
the current no longer depends simply upon the resistance and 
E. M. F., but also depends on the frequency, f , the inductance, 
L, and the capacity, C, that may be contained in the circuit; 
so that Ohm's Law for alternating-current circuits may be sum- 
marized as follows : 

I — The current in any circuit is equal to the electromotive force 
applied to the circuit divided by the impedance of the circuit. 

Let E = E. M. F. or the pressure applied to any circuit, 
Z = impedance of the circuit expressed in ohms, 
I = current strength in that circuit. 



Then, by the above statement, 



current 



or 



pressure 
impedance' 
E 

z ' ■ ' 



(129). 



508 LESSONS IN PRACTICAL ELECTRICITY 

This modification of Ohm's Law, Formula (129), appHes to 
alternating currents flowing in any circuit and bears the same 
relation and importance to alternating-current problems that 
Ohm's Law, I = E -r- R, does to direct-current problems, the 
difference between the two formulae being in the denominator. 

Problem 144. — What current will flow, through a coil of 7 ohms re- 
sistance and 24 ohms reactance when connected across an E. M. F. of 
110 volts, 60 cycles? What current would flow if the coil were connected 
across 110 volts direct current? 

By Formula (124) Z = VsT + Xf = V?^ + 24^ =. V49+576 = 25 ohms. 
By Formula (129) I = - = — — = 4.4 amperes (a). 

By Formula (27) ^ = ^ = ^T = ^^-^ amperes (6). 
K 7 

II — The electromotive force of knowri frequency required to 
maintain a certain current in a circuit of known impedance, is 
numerically equal to the product of the current and the impedance. 

By the above statement, 

pressure = current x impedance, 
or E = I X Z. (130). 

Problem 145. — What E. M. F. would be required from an alter* 
nator of 60 cycles to send a current of 5 amperes through a coil of 4 ohms 
resistance and 0.02 henry inductance? 



By Formula (123) Z = VR^^+JMLJ^ = V42 + (6.28 x 60 x 0.02)2 
= V42 + 7.532 = V16 + 56.7 = 8.52 ohms. 

By Formula (130) E = IxZ=5x 8.52 = 42.6 volts. 

Ill — The impedance, to he inserted in any circuit so that a 
given curre^it will flow by reason of a known pressure, is equal 
to the pressure to he applied divided hy the current that is to he 
maintained. 

By the above statement, 

, pressure 

impedance = , 

current 

or Z = | (131). 

Problem 146. — What would be the impedance of a circuit having a 
pressure of 500 volts across it and having a current of 6.5 amperes flowing 
through it? 

By Formula (131) Z = - = — - = 76.9 ohms impedance. 



ALTERNATING CURRENTS 509 

The similarity between the above formulae and Ohm's 
Law formulae for direct currents will be quite apparent. With 
direct currents the value of the resistance, R, may be calcu- 
lated from the physical dimensions of the wire only, but not 
so with impedance (the total opposition offered to the flow of 
an alternating current), since it does not depend solely upon 
the physical dimensions of the wire, but also upon any induc- 
tance or capacity that the wire may possess. The impedance, 
however, may be measured by the same method as the resistance 
of a direct-current circuit (^ 228), using, of course, an alternating- 
current voltmeter and ammeter, the impedance being calculated 
from Z = E -^ I. Knowing the ohmic resistance of the circuit 
or device, the reactance can be calculated from Formula (125), 
and thereafter the inductance can be found from Formula (122), 
provided the frequency of the current is known. 

351. Impedances in Series. — When several inductive de- 
vices are connected in series on an alternating-current circuit, 
the total impedance of the group cannot be determined by 
adding the individual impedances arithmetically, as is done with 
resistances in direct-current work. Instead, the impedance of 
each device must be resolved into its component resistance and 
reactance, and these are then added separately. 

To FIND THE TOTAL IMPEDANCE OF A NUMBER OF IMPE- 
DANCES CONNECTED IN SERIES! 

Find the sum of the resistances in the circuit, and the sum of the 
reactances; then find the sum of the squares of the total resistance 
and total reactance, and extract the square root of that sum. 

Z = V(Ri + R2 + etc.)' + (Xi + X2 + etc.)2 . . (132). 

-^m5^ — 6 — nm^-^ 

R-4 R = 50 R-2 

X=8 X^O X=6 

2=8.942 2-50 Z-e.66 



Fig. 408. — Impedances in Series. 

Problem 147. — Two inductive and one non-inductive devices are con- 
nected in series, Fig. 408, the coils A and C being the inductive parts 
of the circuit. The values of the resistance, reactance and impedance 



510 LESSONS IN PRACTICAL ELECTRICITY 

of each part of the circuit are inscribed in the figure. What is the total 
impedance of the devices so connected? 

The non-inductive device B has, of course, no reactance, so that its 
impedance is equal to its resistance. If we had added the three impedances 
in the figure we would have obtained the arithmetical sum of 65.6 ohms 
which is incorrect. The correct answer for the total impedance is found by 
Formula (132) to be 

Z = V(Ri + R2 + Rs)^ + (Xi + X2 + X3)2 

= V(4 + 50 + 2)2 + (8 + + 6)2 = V562 + 14^ = 57.7 ohms. 

352. Impedances in ParalleL — When inductive devices are 
connected in parallel, the joint impedance of any given group 
of devices is determined by a similar method to that described 
in If 351; but instead of considering the separate resistances 
and reactances, the opposite properties, conductance and sus- 
ceptance, are considered. In direct-current work, conductance, 
H 107, is the reciprocal of resistance; in alternating-current 
work, the actual conductance of an inductive circuit is not 
taken, but a value termed the effective conductance is sub- 
stituted. 

To FIND THE EFFECTIVE CONDUCTANCE (G) : Divide the resis- 
tance by the sum of the squares of the resistance and reactance. 

« = R^^ (^^^^- 

To FIND THE suscEPTANCE (S) I Divide the reactance by the 
sum of the squares of the resistance and reactance. 

. « = R^^ ••("^)- 

The reciprocal of impedance is called admittance, repre- 
sented by Y, and is equal to the current divided by E. M. F., 
or 

Y=5; (135). 

E 

The relation between admittance, effective conductance and 
susceptance is precisely the same as that between impedance, 
resistance and reactance, explained in K 346, Fig. 402. The 
formula for admittance is therefore analogous to that for 



ALTERNATING CURRENTS 511 

impedance, wherein conductance is substituted for resistance 
and susceptance for reactance; thus, 

Y = VG' + S2 (136). 

To FIND THE JOINT IMPEDANCE OF A NUMBER OF DEVICES 
CONNECTED IN PARALLEL: 

(1) Find the conductances and susceptances of the individual 
devices, (2) find the sum of conductances, (3) find the sum of the 
susceptances, (4) extract the square root of the sum of the squares 
of the total conductance and total susceptance, which gives the 
admittance, (5) since impedance is the reciprocal of admittance, 
divide the admittance into unity to obtain the joint impedance of 
the circuit. Again, 

ioint impedance = , ■ (137). 

V(Gi + G2 + etc.y + (Si + S2 + etc.y 

Problem 148. — What would be the joint impedance of the three de- 
vices in Fig. 408 if they were connected in parallel? 
Effective conductance coil of A is, by Formula (133), 

G = — ^ — = — — - = 0.05, 
R2 + X2 16 + 64 

and its susceptance, by Formula (134), is 

S = ^ =— =0.10. 

R2 + X2 16 + 64 

Since the lamp B is non-inductive, its effective conductance is equal to 
its actual conductance, i.e., the reciprocal of its resistance, 5^0 = 0.02. 
Its susceptance is zero. 

The effective conductance of coil C is, by Formula (133), 

and its susceptance is, by Formula (134), 

S = — ^ = 0.15. 
4+36 

Sum of all the conductances = 0.05 + 0.02 + 0.05 = 0.12. 
Sum of all the susceptances = 0.10 + 0.15= 0.25. 



Admittance (Y), by Formula (136), is Y = Vg^ + S^ = V0.122 + 0.252 
= 0.277; and the impedance is 

1 1 



Y 0.277 



3.6 ohms. 



512 



LESSONS IN PRACTICAL ELECTRICITY 



353. Effective Values of Alternating Currents and E. M. F.*s. 

— We have already seen that an alternating current is one that 
is continually changing its value, as well as reversing its direc- 
tion of flow. It passes through a certain set of values, called a 
cycle, over and over again, the current during each cycle pass- 
ing through a large range of values from zero to its maximum 
value. When it is stated that an alternating current of 10 am- 
peres is flowing in a circuit, some average value must be implied, 
because, as a matter of fact, the current is continually alternating 
through a wide range of values. 

Fig. 409 represents an alternating current whose maximum 
value is 10 amperes. If this current passes through an ammeter 
the deflection wifl be 7.07 amperes, this being the effective value 
of the current. 

The instantaneous values are, as a rule, used very little in 
calculations. In alternating-current apparatus and circuits, 
the E. M. F. spoken of is not the maximum E. M. F., but the 
geometrical average of the E. M. F. values between zero and 
the maximum. On the basis of the sine curve, this average is 
0.707 of the maximum E. M. F. and is termed the effective 
E. M. F. In speaking of alternating voltages, therefore, the 
effective E. M. F. is always meant, and it is this E. M. F. 
which is indicated by measuring instruments. The fluctuations 

of the current are obviously 
too rapid for the needle of 
commercial instruments to 
follow, and the instrument 
therefore indicates the geo- 
metrical mean of the fluctu- 
ating values. 




Fig. 409. — Sucessive Values of a 
60-cycle Alternating Current. 

Maximum value is 10 amperes; effective 
value is 7.07 amperes. 



Consider the current repre- 
sented by' the wave in Fig. 409, 
having a cycle of values between 
A and E. We will also suppose 
that this current is furnished by a 60-cycle alternator, so that the complete 
set of values represented by the cycle included between A and E is passed 
over in eV second. Starting at A the current increases from zero to its 
maximum value at B, then decreases to zero again at C. The impedance 
of the circuit is assumed such that the maximum value of the current is 
10 amperes. It then passes through a similar set of values in the opposite 



ALTERNATING CURRENTS 



513 



direction. The question naturally arises: What are we going to call the 
value of this current? When the current is at its highest value in either 
direction it amounts to 10 amperes, but at all other instants it is smaller 
than this. It is necessary, then, that we understand clearly what is meant 
when we say an alternating current of so many amperes is flowing in a 
circuit. It is easy to see that we must mean some kind of average value, 
since from Fig. 409 we note that the current is continually passing through 
a range of values all the way from its zero value to its maximum value in 
either direction. 

What we are most concerned with in the case of any kind of electric 
current is the effect which it is capable of producing in a circuit, and it 




Fig. 410. 



Effective Value of an Alternating Current. 

Average power is 25 watts. 



has become the universal custom to express alternating currents in terms 
of the value of the direct current which would produce the same heating 
effect. For example, suppose we send 10 amperes direct current through a 
resistance of 2 ohms. The watts dissipated in heat will be I^R = 10^ x 2 
= 200. Now suppose we send an alternating current through the same 
wire and adjust the current until the watts dissipated in heat are 200; 
we will then have what we call 10 amperes alternating current flowing 
through the wire. It is readily seen that the heating effect in a wire wiU 
increase and decrease as the current increases and decreases, because at 
each instant the heating effect will be proportioned to the square of the current at 
■that instant. 

Of course, the current varies so rapidly that to all intents and purposes 
the heating effect appears to be uniform, but it is not hard to see that the 
average heating effect must depend upon the heat produced at each instant 



514 LESSONS IN PRACTICAL ELECTRICITY 

during the cycle. If the frequency is low enough, the variation in the 
heating effect under favorable conditions may be noticed. For example, 
if we connect an incandescent lamp, the filament of which is very fine 
and quite sensitive to changes in the heating effect, to an alternator slowed 
down to yield a current at about 20 cycles, the lamp can be seen to flicker 
perceptibly, but if the frequency be raised above 40, the light becomes 
steady, so far as the eye can judge. 

The variation in heating effect of an alternating current may be repre- 
sented as shown in Fig. 410. Suppose a current, represented by the full- 
line wave, to reach its maximum value of 5 amperes during each half 
cycle or wave; also suppose that this current is sent through an impedance 
of 2 ohms. When the current is at its highest value at B (5 amperes) the 
rate at which heat is expended will be I^R or 5^ x 2 = 50 watts. Lay off 
along BF a distance FG which will represent 50 watts.^ Now take another 
instant during the cycle, as shown at X, and scale off the value of the 
current XY. Having obtained this value, square it and multiply it by 
the impedance (2 ohms), and then lay off XZ to the same scale used for 
FG to represent the watts expended in heating at the instant X. If this is 
done for a number of points, we will obtain a curve of the shape shown by 
the dotted fine. 

This curve shows that the heating effect varies up and down as the cur- 
rent changes. At first it "rises rather slowly as we go along from point A, 
but as the current increases, the heating effect runs up rapidly, because it 
increases with the square of the current. Also note that this curve is 
altogether above the horizontal line, since in squaring the negative values 
of the current we multiply two negative quantities together, giving us a 
positive quantity. 

Coming back to the question of what constitutes the value of an alter- 
nating current, suppose we divide up one section of this curve in Fig. 410, 
between C and E, by a number of equally spaced vertical lines, as shown. 
Then add their lengths together and divide by the number of lines. This 
will give us a fairly correct value of the average length of all the lines. 
The sum of these lines represents 250 watts to the same scale, and dividing 
by 10 lines gives as the average power 25 watts. 

The average so obtained gives us the average watts expended in heat, 
or the average of all the values of I^R. Since R remains the same for all, 

. P . 

it follows that the average watts divided by the resistance, since — = I^, will 

R 

be the average of the squares of all the values of the current at the different 
instants, and the square root of the average of these squares must give the 
value of the alternating current that will produce the same power or heat- 
ing effect as a corresponding direct current. This value of an alternating 
current is sometimes called the square root of mean square value, but it 
is usually called the effective value. 

1 It makes no difference what scale is used in doing this, as long as we 
use the same scale in the laying off of the other points, as the object is 
merely to show how the heating varies. 



ALTERNATING CURRENTS 



515 



In the numerical illustration the average power is 25 watts 
and the resistance is 2 ohms, therefore the average of the 
squares of the current values is ^-^ = 12.5, and its square root 
is 3.54 amperes. This is the effective value of the current. 
In other words, although our alternating current is continually 
rising and falling between the limits + 5 amperes and — 5 
amperes, it only produces the same heating effect in the cir- 
cuit as would 3.54 amperes direct current. 

In the foregoing illustration a current whose maximum 
value was 5 amperes was shown to have an effective value of 
3.54 amperes. The relation between these numbers is as V2 
is to 1. Therefore the effective value of an alternating-current 

is equal to the maximum value multiphed by — - or 0.707; 

V2 

the maximum value of the current is equal to the effective 
value multiplied by V2 or 1.41. 

If we should put an alternating-current ammeter into a 
circuit and the current indicated was 10 amperes, it would 
mean that the effective value of 
the current was 10 amperes 
and that the current was actu- 
ally varying between + 14.1 
and - 14.1 amperes. In the 
same way, if an alternator 




Fig. 411. — Average Value of an 
Alternating Current. 



generates a pressure of 1000 

volts as indicated [by the 

switchboard instrument, the 

effective value is 1000 volts, as indicated, and the maximum 

value of the voltage would be 1000 x 1.41 = 1410 volts. 

Care should be taken not to confuse the effective value of the 
current with the average value. By the effective value is meant 
that value which will produce the same heating effect in a cir- 
cuit as the same value of direct current. By the average value 
is meant simply the average value of all the different values of 
the current during an alternation, as shown in Fig. 411. If 
we draw a number of equidistant vertical lines, add their lengths 
together and divide by the number of lines, we get the average 
length, representing the average current. For a sine wave this 



516 LESSONS IN PRACTICAL ELECTRICITY 

average value is 0.636 times the maximum value. The average 
length of the vertical lines in Fig. 411 is 5 x 0.636 = 3.18 
amperes; if this value is multiphed by the length AC it would 
give the area of the rectangle, ADEC, and this area would be 
equal to the area bounded by the curve ABC and the line AC. 

The average value of an alternating current is simply the 
average of the values during an alternation, but the effective 
value is the square root of the average square of all the different 
values. For convenience the following relations are here given 
together : 

Effective value = 0.707 maximum value; 

Average value = 0.636 maximum value; 

707 

Effective value = =1.11 average value. 

0.636 

The effective value, as shown by the above relations, is slightly 
greater than the average value. 

The reader must not forget that this relation between the 
maximum and effective values applies to sine curves of E. M. F. 
and current only. For other shapes of waves the relation 
might be quite different. A wave w^ith a sharp peak would, 
for example, have a maximum value, which would be much 
higher, compared with the effective value, than given above. 

354. Components of Impressed E. M. Fc — In inductive 
alternating-current circuits there are several distinct potential 
differences, the resultant of which is equal and opposite to the 
applied E. M. F. It has been stated that there is a reactive 
or counter E. M. F. produced by the self-induction of the cir- 
cuit ; to overcome this requires one component of the impressed 
E. M. F. The component of the impressed E. M. F. neces- 
sary to overcome the counter E. M. F. of self-induction will 
be equal and in direct opposition to it. 

Another component is required to overcome the resistance 
of the circuit, which, from Ohm's Law, equals E = I x R. 
We may for convenience imagine the resistance to set up a 
counter E. M. F. which is opposed to another component of 
the impressed E. M. F. (similar to the E. M. F. of self-induc- 
tion). This imaginary counter E. M. F. is directly opposed 
to the ctirrent, consequently the component of the impressed 



ALTERNATING CURRENTS 



517 



E. M. F. necessary to overcome resistance must be in phase 
with the current, that is, in the same direction as the current, 
Fig. 412. 

The relations between the impressed or apphed E. M. F., 
counter E. M. F. of self-induction, and E. M. F. to overcome 
resistance may be shown by means of a triangle, as in Fig. 402, 
the only difference in the values being that all three of the 
former values have been multiplied by the current, so that the 
relations are unchanged. 

In an inductive circuit, we can consider the impressed E. M. F. 
to be composed of two parts or components, one in phase with 
the current and the other at right 
angles to it. The part required to 
overcome resistance is in phase 
with the current and equal to I 
X R; it is represented by the line 
ab in Fig. 412. The part required 
to overcome the counter E. M. F. 
of self-induction is at right angles 
to the current and equal to I X 




S. H^fo Overcome /^es/s^ance 



Phase of 
Current 



Fig. 412. — ComponeDts of 

2"^fL"; iV is represented by the iXti^CirclT""' °" ^" 
line be (at right angles to ab) . The 

diagonal line ac then represents to scale the impressed E. M. F. 
Now since a bc is a ri ght-angled triangle, it follows that the 
length ac = Vab^ + bc^; and since ac = impressed E. M. F., 
ab = resistance drop, and be = reactance drop, the impressed 
E. M. F. = V(I X R)2 + (I X 27rfL)2, or, letting E. = I x R, the 
drop due to resistance, and E; = I x 27rfL, the reactive drop 
due to inductance, the formula for the impressed E. M. F. may 
be written 

E 



V E.2 + E,2 



(138). 



Problem 149. — In Experiment 108, Fig. 403, suppose the drop on the 
lamp is 46 volts and the drop on the inductance coil (resistance neglected) 
is 100 volts; what would be the apphed E. M. F.? 

By Formula (138) 

E = VeTTE^ = V462 + 1002 = V 12116 =110.7 volts. 

From the relations shown in Fig. 412 the following definitions 
may be given for resistance, reactance and impedance: 



518 LESSONS IN PRACTICAL ELECTRICITY 

Resistance is that quantity which when multiphed by the 
current gives that component of the impressed E. M. F. which 
is in phase with the current. 

Reactance is that quantity which when multiphed by the 
current gives that component of the impressed E. M. F. which 
is at right angles to the current. 

Impedance is that quantity which when multiplied by the 
current gives the impressed E. M. F. 

355. Angle of Lag or Lead, and Phase. — In a circuit con- 
taining resistance and reactance, the self-induction also causes 
the current to lag behind the impressed E. M. F., the amount 
of lag depending upon the relative magnitude of the resistance 
and reactance. The amount of this lag is measured as an 
angle, called the angle of lag. It is customary to consider a 
cycle analogous to a circle, and to divide it into so-called 
electrical degrees; thus a quarter of a cycle is 90°, a half cycle 
180°, and so on. This is convenient in that the phase of the 
current with respect to the E. M. F. may be expressed in 
degrees of a circle instead of parts of a cycle. In Fig. 412 it 
appears that the current which is in the direction of ab lags 
behind the impressed E. M. F. in the direction of ac by the 
angle </>, and it is termed the angle of lag of the current in the 
circuit, the angle here being 35°. The tangent of this angle 
is equal to the reactance -^ resistance; hence, if the resistance 
and reactance in a circuit are both known, the angle of lag may be 
calculated from 

reactance 27rfL /..rt^xN 

tan (f) = — : = — — ...... (139). 

resistance R 

9'7rfT 

From the relation , it is seen that the larger the reac- 

R 

tance, compared with the resistance, the larger will be the 

angle of lag, and if the reactance is small in comparison with 

the resistance the angle of lag will be small, the current then 

being nearly in phase wdth the impressed E, M, F. 

Problem 150. — By what angle would the current lag behind the E. M. F. 
in Problem 145? 

Here X = 27rfL = 7.53 ohms and R = 4 ohms, therefore, by Formula (139) 

R 4 



ALTERNATING CURRENTS 



519 




From Table XI, page 236, the angle having a tangent of 1.88 is 62 degrees; 
therefore the current in Problem 145 lags 62° behind the impressed E. M. F. 

The term phase is used to express the angular" displacement in 

degrees between a current and its E. M. F., or between two 

currents or two E. M. F.'s that do not rise 

and fall in unison. Where a current and 

E. M. F. in the same circuit differ in phase, the 

difference is usually expressed as the angle of 

lag or of lead. The action of capacity in a 

circuit is exactly the opposite to that of in- 
ductance. Inductance makes the current lag 

behind the impressed E. M. F., while capacity 

makes the current lead that E. M. F. For 

example: in the upper part of Fig. 413, self- 
induction makes the current, ab, lag behind 

the impressed E. M. F., ac, by the angle (/>. 

Capacity, on the other hand, would make 

the current, ab, lead the impressed E. M. F., 

ac, as shown in the lower diagram of Fig. 413. 

It is possible, therefore, to have a circuit in 

which the ef- 
fects of self-in- 
duction and 

capacity exactly neutralize each 
other. 

In Experiment 106, H 348, Fig. 403, 
the E. M. F., El, across the lamp will 
be in phase with the current, since it 
is a non-inductive resistance; hence, 
in Fig. 414, we can represent Ei by 
the Une, ab, in phase with the current. 
The E. M. F., E2, across the induc- 
tive resistance, M, Fig. 403, will be represented by a line such as ac, con- 
siderably ahead of ab in phase. 

The E. M. F., E3, impressed upon the circuit is the resultant of ab and 
ac, and is represented by the diagonal, ad. The current thus lags behind 
the impressed E. M. F. It is easily seen that the impressed E. M. F., 
E3, is less than the arithmetical sum of Eo and Ei, and also that E3 would 
be equal to the arithmetical sum of Ei and E2 only when E2 and Ei were in 
phase with each other, as would be the case if both devices L and M of 
Fig. 403 were non-inductive, or if a direct current were appHed to the 
circuit. 




Fig. 413.— Dia- 
grams Illustrating 
the Lagging and 
Leading Effect of 
Inductance and 
Capacity Respec- 
tively. 

Upper view, current 
lags behind the e.m.f. 
due to self-induction. 

Lower view, current 
leading the e.m.f. due 
to capacity. 



Current 



Fig. 414. — Diagrammatic Solu- 
tion for Voltage across a Series 
Combination of Resistance and Re- 
actance such as in Experiment 106. 



520 



LESSONS IN PRACTICAL ELECTRICITY 



Take the case illustrated in Experiment 108, Fig. 405. The current in 
lamp Li is the resultant of the currents in the two branches. The current 
in the inductive circuit will lag nearly one quarter of a cycle behind the 
impressed E. M. F., and is represented in Fig. 415 
by the line ab, the line ae representing the direc- 
tion of the apphed E. M. F., E. The current in 
the condenser will be nearly one quarter of a cycle 
ahead of the impressed E. M. F., and is represented 
by the line ac. The inductance of Fig. 405 is as- 
sumed to be adjusted so that ac = ab. The current 
in lamp Li is, therefore, represented by the length 
of the line ad, and it is seen that, because of the 
phase relation' of ac and ab, this current may be 
much smaller than either of the currents in L2 or 
L3 taken by themselves. 




The term phase is generally used also 

when referring to the angular displacement 

between the E. M. F.'s or currents derived 

from alternators. An alternator designed 

to generate a single pressure is called a 

single-phase alternator, a machine designed 

to generate two separate E. M. F.'s for 

sending current through two distinct circuits, so that, at the 

same instant the E. M. F. of one circuit is a maximum while 

the E. M. F. in the other circuit is zero, is called a two-phase 



Fig. 415. — Diagram- 
matic Solution for the 
Total Current in a 
Divided Circuit Con- 
taining Inductance and 
Capacity, Experiment 
108. 



Phase/ 



Phase? 




Fig. 416. — Sine E.M.F. Curves from a 
Two-phase Alternator. 



generator, ^ 360. An arrangement of two circuits (four wires) 
for carrying these currents is termed a two-phase or quarter- 
phase system. The simultaneous pressure curves from the two 
circuits take the form of Fig. 416, the two E, M. F.'s differing 
in phase by 90°. 



ALTERNATING CURRENTS 521 

A system of conductors carrying three single-phase currents 
having an angular displacement of 120°, Fig. 417, is called a 
three-phase system. Such a system requires in practice three 
wires, although theoretically, the system consists of three cir- 
cuits of two wires each; but since the algebraic sum of the 
currents in the three circuits (if balanced) is at every instant 
equal to zero, the three return wires, one on each circuit, may 
be dispensed with, leaving but three wires. 

Any arrangement of conductors carrying two or more alter- 
nating currents definitely related to one another in time con- 
stitute a polyphase system. 



Phase I Phase? Phase 5 




Fig. 417. — Sine E.M.F. Curves of a Three-phase Alternator. 

356. Determination of Power Expended in Alternating-Cur- 
rent Circuits. — In direct-current circuits the power expended 
is the product of the applied E. M. F. and the current. In an 
alternating-current circuit containing ohmic resistance only, 
the current does not lag with respect to the E. M. F., and at 
any instant the power in watts is equal to E x I. With induc- 
tance or capacity in the circuit, the current lags or leads respec- 
tively the impressed E. M. F., the current at times being posi- 
tive when the E. M. F. is negative; hence the actual power 
is reduced. When the reactance is great compared with the 
resistance, the current is 90° away from the E. M. F., so that 
the actual power is zero. 

To FIND THE POWER IN AN ALTERNATING-CURRENT CIRCUIT 
WHEN THE E. M. F. AND CURRENT DIFFER IN PHASE: 

Multiply the effective E. M. F. by the effective current and this 
product by the cosine of the angle of lag or lead. 
Therefore the power is 

P = E X I X cos (140). 



522 LESSONS IN PRACTICAL ELECTRICITY 

The expression cos (j) is the cosine of the angle of lag or lead, and is 
called the power factor. The power factor may he defined as the 
ratio of the real power P to the apparent power E x I. 

The value of cos cj) may be determined from trigonometric 
tables if the angle 4> is known; it may also be derived from the 
relation : j. 

cos = - . . (141). 

Li 

Problem 151. — An alternator generating an E. M. F. of 1100 volts at a 
frequency of 60 cycles supplies energy to a system that has a resistance of 
125 ohms and an inductance of 0.5 henry, (a) Find the value of the 
current. (6) Find the angle of lag. (c) Determine the power factor, 
(d) Calculate the apparent power and the true watts. 

By Formula (123) the impedance is 

Z = VR2 + (27rfL)2 = V1252 + (6.28 x 60 x 0.5)2 =226.1 ohms. 
By Formula (129) the current is 

T E 1100 , „^ , , 

Z ^ 2261 ^ amperes, (a) 

By Formula (139) the tangent of the angle is 
, ^ 27rfL 6.28 x 60 x 0.5 188.4 . _, 
^^^^ = -^ = 1^^ = 1^ = l-^l- 

From Table XI, the angle whose tangent is 1.51 is = 56.5°. (b) 
By Formula (141) the power factor is 

cos (f) = - = • = 0.55 or 55 per cent, (c) 

^ Z 226.1 

Apparent power, by Formula (54), is 

P=ExI=1100x 4.86 = 5346 volt-amperes, (d) 

True watts, by Formula (140), are 

P = E X I X cos = 1100 X 4.86 x 0.55 = 2940.3 watts, (d) 

To measure alternating-current power it is necessary to 
know the angle of lag or lead if separate voltmeters and 
ammeters are used, or to employ a wattmeter, which gives 
the true power directly. The rating of alternators and trans- 
formers is usually expressed in terms of the apparent power, 
that is, in kilovolt-amperes (abbreviated kv-a). 

The effect of difference of phase, or the lagging of the current behind 
the E. M. F., upon the power expended may be more clearly shown by the 
sine curves in Figs. 418 to 420. Fig. 418 shows the conditions in a cir- 



ALTERNATING CURRENTS 



523 




>\ 


/I 


\ 

\ 
\ 


-7 

/ 



Fig. 418. — Curves of E.M.F., Current 
and Power in an Alternating-current Cir- 
cuit Containing only Resistance. 



cuit containing ohmic resistance only, the current wave being in phase 

with the impressed E. M. F. wave; the power curve or wave lies wholly 

above the horizontal axis. The power is positive at all times, since the 

product of the positive values 

of E. M. F. and current as 

well as the products of their 

negative values are always 

positive, and its effective 

value is simply the product 

of the effective E. M. F. and 

the effective current, as read 

on a voltmeter and ammeter; 

that is, power = E x I. This 

represents the condition when 

the current is flowing through 

a non-inductive resistance. 

Suppose, however, that the 
circuit contains inductance, 
the current lags behind the 
E. M. F. by an angle less than 
90°, Fig. 419. The power 
curve is here constructed as before, but it -is no longer wholly above the 
horizontal axiG, due to the fact that the current curve at times is positive 
while the E. M. F. curve is negative; consequently the product of their 

values at those instants 
are negative, and the 
corresponding points on 
the power curve lie below 
the horizontal. This 
means that during the 
intervals of time, ab and 
cd, negative work is 
being done; or, in other 
words, the circuit during 
those intervals, instead 
of having work done on 
it, is returning energy to 
the system to which it is 
connected. In Fig. 420 
the angle of lag has be- 
come 90°, the reactance 
being great and the resistance neghgibly small. In this case the power 
curve lies as much above the horizontal axis as below it, the circuit return- 
ing as much energy as is expended in it; the negative power from c to d 
being equal to the positive power from b to c. The total work done in this 
case, therefore, is zero, and although a current is flowing, this current does 
not represent energy expended. 




Fig. 419. — Curves of E.M.F., Current and 
Power in a Circuit Containing Inductance. 



524 



LESSONS IN PRACTICAL ELECTRICITY 



The current may be looked upon as being resolved into two compo- 
nents, Fig. 421, one at right angles to the E. M. F., known as the reactive 




Fig. 420. — Curves of E.M.F., Current and Power in 
an Inductive Circuit Containing Negligible Resistance. 

The current lags 90° behind the impressed E.M.F. 



component of the current, and the other in phase with the E. M. F., known 
as the adive component. From Fig. 421 it will be seen that the greater 
the angle of lag of current behind the impressed E. M. F. the greater will 

be the reactive component and the smaller 
will be the part which is expending power 
in the circuit. 

Although reactive currents do not rep- 
resent any power wasted, they are ob- 
jectionable, as they merely load up the 
generator and lines, thus limiting their 
output as to current-carrying capacity. 
For example, an alternator furnishing cur- 
rent to a system having a very low 
power factor may be delivering a small 
amount of power, so that little power 
would be required to drive the alternator. 
At the same time the current is circu- 
lating through the lines and the armature 
of the alternator, thus heating the line 
wires and heating the machine also. As the current output of the armature 
is limited to a great extent by this heating, it is seen that the useful current 
which may be taken from the alternator is cut down by the presence of 
this reactive current. In practice, alternating-current apparatus is always 
designed so as to have as large a power factor as possible consistent with 
other requirements. It is often possible to cut down the effect of self- 




Reaciive Component 
Fig. 421. — Diagram Illus- 
trating the Active and Reac- 
tive Components of an Alter- 
nating Current in a Circuit. 



ALTERNATING CURRENTS 525 

induction in the circuit by inserting a condenser, thus cutting down the 
lag of the current and increasing the power factor. If the capacity of the 
condenser is sufficient it is possible to completely neutralize the effect of 
inductance, in which case the current would be in phase with the im- 
pressed E. M. F., and the circuit would be said to be tuned for the par- 
ticular frequency. 



QUESTIONS 

1. How does an alternating current differ from a continuous or direct 
current? 

2. What advantage has the alternating current over the direct current? 

3. What do you understand by the term frequency? 

4. How would you determine the frequency of any alternator? 

5. Why does self-induction have such an important effect upon 
an alternating current? 

6. What is impedance? 

7. How would you represent graphically the relation existing between 
impedance, reactance and resistance? 

8. If the frequency of an alternating E. M. F. that is impressed upon 
an inductive circuit is doubled how will the current be affected, the voltage 
remaining the same? 

9. What is meant by the capacity of a line or circuit? 

10. What effect has capacity upon the flow of an alternating current? 

11. What is the essential difference between capacity and inductance 
upon the flow of an alternating current? 

12. Does Ohm's Law as applied to direct currents hold true for alter- 
nating currents? 

13. What factors beside resistance must be taken into consideration 
in determining the flow of alternating current? 

14. What is the general form of Ohm's Law for alternating-current 
circuits? 

15. How can the impedance of a circuit be measured? 

16. What is admittance? 

17. What is meant by the effective value of an alternating current? 

18. What are the components of the impressed E. M. F.? 

19. Give a graphical illustration of the relations existing between 
the impressed E. M. F. and its components. 

20. Define resistance, reactance and impedance. 

21. What is meant by angle of lag? 

22. Under what conditions can a current in a circuit lead the E. M. F. 
impressed upon it? 

23. Knowing the values of the resistance and the inductance of a circuit, 
how would you determine the angle of lag for a current of given frequency? 

24. Will the product of volts by amperes give the true power expended 
in an alternating-current circuit? Why? 

25. What is meant by power factor? 



526 LESSONS IN PRACTICAL ELECTRICITY 



PROBLEMS 

1. An ammeter in a certain circuit indicates 15 amperes. What 
would be the maximum value of this alternating current. Ans. 21.15 
amperes. 

2. An alternator has 24 poles and its armature rotates at a speed of 300 
revolutions per minute, (a) What will be the frequency? (6) How many 
times would the current change its direction in one minute? Ans. (a) 60 
cycles; (6) 7200. 

3. (a) What would be the impedance of a circuit of 20 ohms resis- 
tance and 10 ohms reactance? (6) If a 60-cycle E. M. F. of 110 volts is 
applied to the above circuit what current will flow? (c) What is the induc- 
tance of the circuit? Ans. (a) 22.3 ohms; (b) 4.93 amperes; (c) 0.026 
henry. 

4. (a) What would be the impedance of the circuit in Problem 3 if 
a 50-microfarad condenser were inserted in series? (6) How much current 
would flow? Ans. (a) 47.42 ohms; (6) 2.33 amperes. 

5. What E. M. F. must an alternator of 60 cycles supply to a circuit 
of negligible resistance and having an inductance of 0.2 henry in order 
that a current of 5 amperes may flow? Ans. 376.8 volts. 

6. (a) What would be the impedance of a circuit consisting of two 
coils, A and B, and two lamps, all connected in series; coil A has a resis- 
tance of 2 ohms and a reactance of 0.5 ohm; coil B has a resistance of 
4 ohms and a reactance of 7 ohms; each lamp has a resistance of 50 ohms. 
(6) What would be the impedance of each part of the circuit? Ans. (a) 
108.17 ohms. (6) A = 2.03 ohms, B = 8.06 ohms, lamps = 50 ohms each. 

7. What would be the impedance of the circuit if the coils and lamps 
in Problem 6 were connected in parallel? Ans. 1.7 ohms. 

8. (a) What will be the reactance of a coil of wire having a resis- 
tance of 4 ohms and an inductance of 0.02 henry, when connected to a 
60^cycle alternating E. M. F. of 110 volts? (b) What current will flow? 

(c) By what angle will the current lag behind the impressed E. M. F.? 

(d) How many watts will be expended? (e) What is the value of the power 
factor of the circuit? (/) If the coil is connected to 110 volts direct current, 
how much current will flow? Ans. (a) 7.54 ohms. (6) 12.89 amperes, 
(c) 62°. {d) 652.23 watts, (e) power factor = 46 per cent. (/) 27.5 
amperes. 



LESSON XXIX 

ALTERNATING-CURRENT APPARATUS AND MACHINERY 

Transformers — Transformer Regulation and Efficiency — Transformers on 
Polypl^ase Circuits — Alternators — Revolving- Armature Alternators 

— Revolving-Field Alternators — Inductor Alternators — Power Rat- 
ing of Alternators — Conversion — Rotary Converters — Rectifiers 

— Questions and Problems. 

357. Transformers. — A transformer is a device for trans- 
forming electrical energy at one voltage into electrical energy 
at another voltage, and consists of two electrically-distinct 
windings which are so arranged that the magnetic flux asso- 
ciated with one winding also threads through the other. 
When an alternating current is passed through one wind- 
ing the magnetic flux first rises to full value in one direc- 
tion, falls to zero, rises again to a maximum value in the oppo- 
site direction, and falls again to zero, and so on; this varying 
magnetic flux induces in the other winding an alternating 
E. M. F. In the induction coil, ^ 263, a make-and-break device, 
or interrupter, was necessarily included in one winding in order 
to vary the strength of the magnetic field and thus produce 
an E. M. F. in the other winding, because the induction coil 
is operated on direct-current circuits. The transformer, how- 
ever, requires no interrupter, since the change in flux is accom- 
plished by the alternating current itself. The two windings are 
termed the primary and the secondary, the primary being the 
winding which receives the energy from the supply circuit 
and the secondary that which receives the energy by induction 
from the primary. In most transformers the two windings are 
magnetically^ linked by a closed core of laminated iron. 

The construction of transformers for single-phase circuits is 
shown in Fig. 422; three types are illustrated, namely the core, 
shell and combined core and shell types. The cores are built 
up from annealed punchings of thin silicon sheet steel with 

527 



528 



LESSONS IN PRACTICAL ELECTRICITY 



the joints staggered so as to yield a core of low reluctance and 
small iron loss. The two windings are well insulated from 
each other by a thick shield of layers of mica, or other suitable 



,'Core 




fPrimary 

(^Secondary 



Core- 

Primoiry- 
Secondary ■ 




Primary ^ 



Core 




Left 



Secondaryy 
Fig. 422. — Types of Transformers. 

core type; center — shell type; right — combined core and shell type. 



insulating material, of sufficient size to project beyond the 
windings. The turns and layers of each winding are insulated 
from each other by various materials to thicknesses depending 
on the voltage of the circuit to which they are connected. The 

windings are usually subjected to a 
vacuimi-drying and filling process 
which removes all moisture and then 
impregnates the coils with an in- 
sulating compound under pressure. 
The transformers are placed under 
oil contained in an iron tank, the oil 
being used for insulating purposes 
and for cooling the transformer in 
order to avoid high temperatures 
which would injure the transformer 
insulation. The heat generated in 
the smaller sizes of transformers 
is conveyed to the case by the oil 
and is there dissipated by radiation and natural air circulation. 
The case for such self-cooled transformers is of cast-iron or 
pressed steel of the form shown in Fig. 423. Such transformers 
beyond 50 kw. require increased radiating surface, and there- 
fore the tank is universally made in the form of corrugated 
steel [tanks. For the larger sizes external oil-circulating tubes 
or radiators are used on the tanks, the latter type being shown 
in Fig. 424. Large transformers may also be cooled by placing 
coiled pipes in the oil at the top of the transformer tank and pass- 




Fig. 423. —Wagner 15-kw 
220-2200-volt Pole-type Dis- 
tributing Transformer. 



ALTERNATING-CURRENT APPARATUS 



529 



ing air or water through these pipes; the latter are called water- 
cooled transformers. Transformers which are not submerged 
in oil may be cooled by cur- 
rents of air circulated past 
the windings and core by 
means of a blower; these are 
called air-blast transformers. 
The function of trans- 
formers is to change the vol- 
tage from, one value to 
another, this being accom- 
plished by having more turns 
on one winding than on the 
other. Thus, if the primary 
winding has 200 turns and 
the secondary has 1000 turns, 
then the voltage available at 
the secondary terminals will 
be 1000 ^ 200 = 5 times as 
great as the E. M. F. im- 
pressed upon the primary. 
The ratio of the number of 
turns, n2, in the high-voltage 
winding to the number, m, 

in the low-voltage winding is called the ratio of transformation, 
and is given by the equation 

where Ei and E2 are the respective voltages of the two windings. 
When the transformer is used to deliver energy at a higher 
voltage than that at which energy is received it is called a 
step-up transformer, and when it lowers the voltage it is called 
a step-down transformer. Any desired alternating E. M. F. 
may be procured by properly proportioning the number of 
turns on the windings of a transformer. 

If there were no losses in a transformer, its power output 
would be the same as its power input. Since power is equal to 
volts times amperes (at unity power factor), it follows that 
P = El X Ii = E2 X I2 (143). 




Fig. 424. — General Electric Co., 
1000-kw. Self-cooled Transformer. 



530 



LESSONS IN PRACTICAL ELECTRICITY 



where Ii and I2 are the currents in the low- and high-tension 
windings respectively. From this equation 

El _ I2 

E2 Ii 



(144), 



r'S 



I f= 50 Amps 




> < 




If /O Amps 


£-- IZO ' 

^voifs ; 


77 


— 


1 t 

: 4^00 

\ Volts 


rt • f 


'' v^ 




Primary--' 
rij --ZOOTums 








"^Secondary 
n 2-1000 Turns 



Fig. 425. — Voltage and Current 
Relations in a Transformer. 



or the ratio of voltages is the inverse ratio of the currents in the 
two windings. Thus, if 50 amperes traverse the primary wind- 
ing of the transformer above 
mentioned, the secondary cur- 
rent would be one-fifth as great 
or 10 amperes. These values 
are indicated in Fig. 425. 
Since all transformers have 
losses, namely: eddy-current 
and hysteresis losses in the 
core and PR losses in the 
primary and secondary wind- 
ings, equation (144) is not exact, but as the efficiencies of trans- 
formers, \ 358, are very high — over 95 or even over 98 per cent 
■ — this equation may be used for most practical calculations. 

Problem 152. — The primary voltage of a 10-kw. transformer used to 
supply electricity to 110-volt lamps is 2200 volts. What is the ratio of 
this transformer and what are the full-load currents in the two windings, 
neglecting losses? 

In this step-down transformer which supplies a circuit of unity power 
factor: Ei =110 volts, E2 = 2200 volts, and P = 10,000 watts, therefore 
from equation (142) 

E,^2_200^ 
El 110 



and from equation (143) Ii = 



P 10,000 



El 



and 



Eg 



110 
10,000 
2200 



= 91 amperes. 



= 4.5 amperes. 



Transformers are much used in transmitting and distributing 
electrical energy over long distances, for efficiency demands high 
line voltages in order to reduce the fine losses, \ 334. At the 
power station the generator voltage is raised by step-up trans- 
formers to the value found economical for transmission, and 
at the receiving substations the fine voltage is lowered by step- 



ALTERNATING-CURRENT APPARATUS 531 

down transformers to values suitable to the apparatus supplied 
with energy, such as motors, rotary converters, lamps, etc. 

For some purposes a part of the same electric circuit is used 
for both primary and secondary windings of the transformer, 
in which case it is called an auto-transformer, Fig. 426. The 
ratio of transformation is the ratio of the number of turns 
included between the high-voltage terminals and the number 
between the low-voltage terminals, Fig. 426. Such transformers 
are used in starting induction motors, ^ 370, for compensators 
for varying the E. M. F. of alternating-current circuits over 
limited ranges, and for other purposes 
where small transformation ratios are re- ip, Turns 

quired. 

Another type of transformer which is ^ 
used in connection with incandescent light- 
ing on series circuits and with electrical 
measuring instruments is called a current 
transformer. When used for the latter Fig. 426. — Connec- 
purpose the primary winding is connected tions of an Auto-trans- 
in series with the circuit of which the cur- 
rent is to be measured, and the secondary is connected directly 
with the ammeter terminals. The instrument will then carry a 
current proportional to but much less than the main current and 
will not be subjected to the high voltage of the main circuit. 

358. Transformer Regulation and Efficiency. In constant- 
potential transformers the regulation is the ratio of the rise of 
the secondary terminal voltage from rated load to no load (at 
the specified power factor and constant impressed primary vol- 
tage) to the secondary terminal voltage at rated load. For 
example, the secondary voltage of a transformer rises from 220 
to 230 volts on the removal of rated load; its regulation is 
(230-220) ^ 220 = 0.045 or 4.5 per cent. 

The primary winding of a transformer possesses a high inductance since 
it is a coil wound on an iron core. Hence, when an alternating pressure 
is appUed to the primary terminals, a current flows through the primary 
and produces an alternating magnetic flux in the core; this flux induces a 
counter E. M. F. in the primary which is nearly equal and in direct oppo- 
sition to the applied pressure, and with the secondary circuit open only a 
very small current can flow through the primary. This small current 
in the primary, however, is suflScient to set up the alternating flux in the 



532 LESSONS IN PRACTICAL ELECTRICITY 

core and induce an E. M. F. in the secondary {^ 357) in addition to the 
counter E. M. F. of the primary. This induced E. M. F. in the secondary 
is in the opposite direction to the E. M. F, appHed to the primary and 
consequently when the secondary circuit is closed by connecting a load 
to it, a current flows through the secondary in the opposite direction 
to the current in the primary. The secondary current also tends to pro- 
duce an alternating flux in the core, which flux is in a direction opposite 
to that produced by the primary (Lenz's Law, ^ 251). The effect of the 
opposing flux set up by the secondary current is to decrease the total 
flux in the magnetic circuit, which decreases the counter E. M. F. induced 
in the primary, thus permitting a greater primary current to flow. The 
decrease in magnetic flux and in the primary counter E. M. F. in com- 
mercial transformers between rated load and no load is very small, since 
a very small decrease of the primary counter E. M. F. greatly increases the 
difference between the applied primary pressure and its counter E. M. F. 
so that the primary current is greatly increased. In fact, the increase of 
primary current due to the loading of the secondary is just great enough 
(or very nearly) to exactly balance the demagnetizing action of the current 
in the secondary winding; that is, the flux in the core must be maintained 
approximately constant by the primary current whatever value the second- 
ary current may have. When the load on a transformer is increased, the 
primary of the transformer automatically takes additional current and 
power from the line in direct proportion to the load on the secondary. 

If the impressed primary voltage is maintained constant, it 
may be assumed that the secondary voltage of a well-designed 
transformer will remain practically constant at all loads. There 
is, however, a slight drop in secondary voltage from no load 
to rated load, which may vary from 1 per cent to 5 per cent, 
depending on the design and characteristics of the transformer. 
The voltage drop varies almost directly as the load, provided 
the power factor remains constant. On non-inductive load 
(that is, with a load of 100 per cent power factor) the regu- 
lation, as a rule, exceeds the resistance drop by only a small 
amount. However, with transformers having high reactance 
this is not the case, since the reactive component of the voltage 
adds considarably to the resistance drop. On inductive load the 
regulation depends chiefly upon the reactive drop; hence, the 
less the reactive drop, the better the regulation and vice versa. 

The efficiency of a transformer is a ratio of the power out- 
put at the secondary terminals to the power input at the primary 
terminals. To determine the efficiency of a transformer directly 
by measuring the input and output, does not constitute a satis- 



ALTERNATING^CUHRENT APPARATUS . 533 

factory method when the efficiency is high. A more accurate 
method is by measuring separately by a wattmeter, the core 
and copper losses. The core loss is measured by placing a 
wattmeter in the primary circuit with the secondary circuit 
open. The copper loss is measured by placing a wattmeter 
in the primary circuit and with the secondary short-circuited 
through an ammeter, applying just enough pressure to the 
primary to cause the full-load current to flow in the secondary. 
The losses being known, the efficiency at any load is readily 
found, bearing in mind, however, that the iron loss is a con- 
stant quantity and the copper loss varies as the square of the 
load. The formula for the efficiency of a transformer is : 

efficiency = — — ; . . (145). 

output + copper and n^on losses 

Problem 153. — If the transformer in Problem 152 has a copper loss of 
175 watts and an iron loss of 150 watts when it is delivering its rated 
output of 10 kw., what is its efficiency? 

By Formula (145) 

^ . output 10,000 10,000 ^^ ^ 

efficiency = = — = — = 96.8%. 

output + losses 10,000 + 175 + 150 10,325 

359. Transformers on Polyphase Circuits. — The connection 
of transformers to polyphase circuits may be accomplished in 
many ways, but only a few of the simpler methods will be here 
considered. Fig. 427 shows the connection diagrams of single- 
phase transformers applied to two- and three-phase circuits; 
the ratio of transformation is assumed as 10 and numerical 
values are assigned to the voltages and currents for illustration. 
At (a) are shown the connections of two transformers to a four- 
wire two-phase 1000- volt system in order to transform to a 
three-wire two-phase circuit. The voltage between the outer 
low-tension terminals is IOOV2 or 141 volts. 

On three-phase circuits either a single three-phase transformer 
or three single-phase transformers may be used to alter the 
voltage of the system; the latter plan is assumed in Fig. 427. 
The three transformers may have their primaries connected to 
the three-phase supply circuit in Y as shown at (b), or in A 



534 



LESSONS IN PRACTICAL ELECTRICITY 



2 phase System 



S-Pticrse Circuit 



10 Amps 100 A mps 




d-Phase Circuit 





1 


10 

1 






1 




4 




(b) 





3- Phase Circuit 





2-Plnase System 



■^ 




CQ 




\ ^ 


w 




^ 


i 1 


q; 






1 1 




k «^ 








^ s 








:S ^ 








§ 5 
















^ 1 





'^--300 Amps 






TT 






Fig. 427. — Connections of Single-phase Transformers on Two- 
and Three-phase Circuits. 

(a) 4-wire 2-phase to 3-wire 2-phase transformation, (b) 3-phase Y-connection. 
(c) 3-phase A-connection. (d) 3-phase Y- to A-transformation. (e) 2-phase to 
3-phase Scott transformation. 



(delta) as shown at (c). If the voltage between any pair of line 

E 



wires is E volts, then the voltage across each primary is 



V3 



for the Y-connection and E for the A-connection; and if the 



ALTERNATING-CURRENT APPARATUS 535 

current in each line wire is I amperes, then the current in each 

primary winding is I for the Y-connection and — — for the A- 

v3 

connection. The primary and secondary windings of the 
three transformers may both be connected Y, both A, or one 
set of windings Y and the other A. At (d) are shown the con- 
nections of three single-phase transformers with their primaries 
connected in Y and their,' secondaries connected in A. A 
scheme for transformation from a two-phase four-wire system 
to a three-wire three-phase system is shown at (e); the upper 
transformer must have a tap at the middle point of its second- 
ary and the lower transformer must have a ratio of 10 to 
iVs, or 11.5. 

360. Alternators. — Alternating-current generators, or alter- 
nators, must, like direct-current generators, have field magnets 
and an armature; but the commutator of the direct-current 
machine is replaced by slip rings on the alternator in which 
the armature or field revolves. The windings of the revolving 
armature are connected to slip rings, and the alternating 
E. M. F.'s generated in the windings are delivered to the 
external circuits by means of the brushes resting on the slip 
rings. In alternators in which the field revolves, the slip rings 
carry the direct current, obtained from a separate source, to 
the field windings. 

Alternators may be classified according to construction into 
three types: 

1. Revolving armature and stationary field magnets; 

2. Revolving field magnets and stationary armature; 

3. Stationary armature, stationary field winding, and a 
revolving mass of iron termed an inductor; this mass of iron 
has polar proj ections that extend radially outward so as to drag 
the magnetic flux set up by the stationary field winding past 
the armature conductors. 

All alternators must have direct current for field excitation, 
the direct current being derived from a separate generator 
termed an '' exciter," the machine being used for field excita- 
tion only. In some types of alternators, the armature, in addi- 
tion to the alternating-current winding, has a separate winding 



536 



LESSONS IN PRACTICAL ELECTRICITY 



connected to a commutator for producing the direct current 
for tiie field excitation, thus making the alternator self-exciting. 
The field structure of alternators is multipolar and may con- 
sist of as many as 60 or more poles in machines direct- 
connected to a slow-speed engine; on the other hand, in 
machines driven by turbines at high speed the number of poles 

may be very small. The 
frequency of the E. M. F.'s 
produced by any alternator, 
If 342, is obtained by mul- 
tiplying the number of pairs 
of poles (half the number of 
poles) by the number of 
revolutions per second of 
the revolving member. 

Alternators may also be 
classified according to de- 
sign into: 
1. Single-phase alternators, 
- 2. Polyphase alternators. 
In a single-phase winding 
all the inductors are con- 
nected in series so that their 
individual E. M. F.'s will 




Fig. 428. — Self-exciting Alternator of 
. the Revolving Armature Type. 



add, the two remaining terminals of the armature winding being 
connected one to each of two slip rings. The windings on the 
armature core of a polyphase alternator are separate and distinct 
for each phase and properly distributed over the armature sur- 
face, all the inductors of any one phase usually being in series 
with each other. A three-phase alternator, for example, delivers 
three equal and separate E. M. F.'s, which are displaced from 
each other in time by one-third of a cycle. Fig. 428 shows a 
three-phase alternator of the revolving armature type; every 
pair of the three slip rings yield a definite alternating voltage. 
361. Revolving-Armature Alternators. The armatures of 
revolving-armature alternators are similar in construction to 
those used in direct-current generators but are less complicated 
because they have fewer coils and do not require commu- 
tators with their many connections. The armature cores are 



ALTERNATING-CURRENT APPARATUS 



537 



built up from laminations or slotted punchings to form a slotted 
core, and form-wound coils are placed in the slots. The number 
of inductors is an even multiple of the number of poles, and the 
groupings are symmetrical with respect to each pair of poles. 
The revolving-armature type of alternator that is self- 
exciting has two distinct windings on the armature ; one winding 
for generating the alternating E. M. F. and connected to slip 
rings, and the other winding for furnishing the direct-current for 
field excitation, this winding being connected to a commutator. 




Fig. 429. — Armature of Self-exciting Alternator. 

An alternator of this type is shown in Fig. 428 and its armature 
is depicted in Fig. 429. Alternators of this type are wound 
for two- or three-phase service; to secure single-phase service 
from a three-phase alternator the load is connected between 
any two legs of the three-phase windings. Such alternators 
when run single-phase yield about 70 per cent of their three- 
phase capacity. 

In Fig. 430 are shown simple diagrams of single-, two- and 
three-phase windings of a multipolar alternator. In these dia- 
grams the heavy radial lines represent the inductors, and the 
other Unes the connecting wires. Where only one inductor is 
shown, in practice there would be a number placed in one slot 
or distributed over several slots. These windings would also 
apply to the main winding of an armature having an exciter 
winding. 

362. Revolving-Field Alternators. — In generating an E. M. 
F. there must be a motion of either the inductors or the 
field magnets, ^ 275, and it is quite as common in alternators 
to have the field magnets revolve inside a stationary armature 



538 



LESSONS IN PRACTICAL ELECTRICITY 



as to have the armature revolve. Revolving-field alternators, 
one of which is shown in Fig. 307, Lesson XXIII, have become 
the recognized standard for alternators of large output, since 
the stationary armature windings can be more easily insulated 
to withstand high voltage, and the collection of high-tension 




Single- Phase Winding 



Two-Phase Winding 




Three-Phase Winding 
Fig. 430. — Armature Windings of Alternators. 

armature currents from the slip rings is avoided. Revolving- 
field alternators can be constructed to generate 25,000 volts, 
and machines that are required to give either high voltage or 
large currents are of the revolving-field type, the revolving- 
armature type of construction being usually restricted to 
machines of 25 kw. or less. 



ALTERNATING-CURRENT APPARATUS 



539 



The revolving field consists of laminated sheet iron pole 
pieces bolted to- a cast steel or iron ring, which is connected to 
the hub by spider arms. The pole pieces have a wide face so 
as to secure not only a wide polar arc for the proper distribu- 
tion of the magnetic flux, but also to hold the field windings in 
place, the field winding being wound on spools which are slipped 




Fig. 431. 



Portion of Armature of a Revolving- 
field Alternator. 



over the pole pieces before they are bolted to the ring. The low- 
voltage direct current for field excitation is led to the winding 
through two collector rings. 

The stationary armature consists of a circular cast-iron frame 
inside of which are dovetailed sheet-iron laminations. The 
laminations are stacked together and held rigidly in place by 
steel clamping fingers, ducts being provided at frequent inter- 
vals in stacking to allow for the free circulation of air. The 



540 



LESSONS IN PRACTICAL ELECTRICITY 



inner surface of the laminations is slotted to receive the wind- 
ings, consisting of carefully insulated form-wound coils, which 
are held in the slots by suitable wedges. The method of 
assembling the armature coils is illustrated in Fig. 431, which 
shows a portion of a stationary armature. The armature coils 
are usually connected to furnish two- or three-phase currents. 

363. Inductor Alternators. — A modification of the station- 
ary-armature type of alternator is the inductor type in which 
neither the armature nor field windings move, the only moving 
part being a mass of laminated iron having polar projections. 



^- Armature-Coils ^^-^ 



Field Coil- 




^ r^ 

Fig. 432. — Arrangement of Inductor Alternator, 

These projections are magnetized by a direct current flowing in 
a single annular field coil clamped in position in the center of 
the machine. The schematic arrangement of parts is shown in 
Fig. 432. The field coil is wound on a copper or brass bobbin, 
which not only protects it mechanically, but also protects it 
electrically at such times when the field circuit is broken, as the * 
E. M. F. of self-induction at those instants might be high 
enough to puncture the insulation. The metallic bobbin acts 
as a single-turn coil surrounding the decaying magnetic flux, 
and thus prevents high E. M. F.'s of self-induction in the field 
winding. 

The circular armature frame surrounding the inductor has 
internal projections forming the cores of the armature coils; 
their projections are equal in number and size to the inductor 
projections. The armature coils are form wound and laid in 
grooves in the armature cores in a manner similar to that of re- 
volving-field machines. The distinguishing characteristic of the 



ALTERNATINO-CURRENT APPARATUS 541 

inductor alternator is that any one set of armature coils or 
portion of armature inductors is subjected to a magnetic flux 
of one polarity only, the magnetism fluctuating from a mini- 
mum to a maximum, the magnetic flux being a maximum 
through the armature coils when the pole faces of the inductors 
are directly opposite the faces of the armature poles, and the 
flux a minimum when the inductors are in an intermediate 
position. As the inductors revolve, the magnetic flux varies 
from minimum to maximum and back again but does not 
reverse its sign since there is only a single field coil. 

The advantages claimed for the inductor alternator are 
absence of any moving wire, thus reducing the danger of chaf- 
ing the insulation, absence of collector rings and therefore of 
brush friction, and increased facilities for insulation. These 
advantages are offset by the fact that only half as great a pres- 
sure is obtained by a given flux as would be obtained in the 
ordinary type of machine, and by the large eddy current loss 
and bad regulation. This type of alternator has become nearly 
obsolete, except in special cases, such as high-frequency alter- 
nators for radiotelegraphic systems employing undamped waves, 
11381. 

364. Power Rating of Alternators. — Alternating-current 
generators are usually rated in kilo volt-amperes (kv-a.) instead 
of kilowatts, because it would be impossible for the manufac- 
turer to know in advance the amount of inductance and 
capacity of the circuits to which the alternator is required to 
furnish power. The actual energy output in kilowatts is equal 
to the apparent power or kilovolt-amperes multiplied by the 
power-factor of the circuit. An alternator having a rating of 100 
kv-a. would deliver under fufl-load conditions 100 kilowatts at 
unity power factor; but if the power factor should be 0.8 the 
energy output of the machine would be reduced to 80 kilo- 
watts, for the current and consequently the heating of the 
armature would be approximately the same as if it were deliver- 
ing 100 kilowatts at unity power factor. 

365. Conversion. — The economical operation of large elec- 
trical systems involving the generation, transmission and dis- 
tribution of large amounts of electrical energy requires that the 
energy be generated as alternating current in one or more large 



542 LESSONS IN PRACTICAL ELECTRICITY ; 

central stations. The alternating current is transmitted at high I 

voltage to points where it is to be used, and there stepped down j 

through transformers to suitable commercial voltages. The | 

ease with which the voltage of alternating currents can be 1 

changed with transformers has resulted in the almost uni- | 

versal use of such currents in transmission systems. But 1 

alternating current cannot be used to perform all the services ' 

in which electricity takes part, for example the electrolytic ; 

action required in the refining of metals, in electroplating, and ' 

in the charging of storage batteries requires direct current, i 

Thus there is frequent need for converting the alternating cur- \ 

rent into a direct current. The alternating current generated in ; 

central stations supplying power to street railway systems, \ 

must in many cases, be converted into a direct current, because ; 

the railway equipment is of the standard direct-current type j 

so well suited to city traction systems. The future development j 

of the alternating-current series motor, however, will probably ] 

reduce this need for current conversion. ] 

The conversion of large amounts of alternating-current ] 

power to direct-current power is made by the use of synchronous ; 

converters, generally called rotary converters, H 366. A converter, ; 

in general, is a machine employing mechanical rotation in ' 

changing electrical energy from one form into another. In j 

addition to the synchronous converter mentioned above, which j 

may be used to convert from alternating to direct current or i 

vice versa, another form of converter known as a motor-generator ; 

set, II 375, may perform the same function. The conversion of | 

small amounts of power is considered in Ij 367. I 

366. Rotary Converters. — The rotary converter is essen- j 

tially an alternator and a direct-current generator combined in | 

one machine, the general appearance of which is similar to that | 

of a direct-current generator. It has, in addition, suitable col- ! 

lector rings connected to the armature winding at points hav- \ 

ing the proper angular relation, the number of rings depending ; 

on the number of phases on which the machine is operated, i 

It was shown in Lesson XXIII that the armature windings of i 

a direct-current generator have an alternating current flowing : 

through them and that, by properly connecting these windings ; 
to a commutator, the alternating current is commuted to a 



ALTERNATING-CURRENT APPARATUS 



543 



direct current at the brushes. Therefore, if the winding of the 
revolving armature of an alternator is tapped at the proper 
points and connected properly to the segments of a commuta- 
tor a direct current will be delivered to a set of brushes bear- 
ing on the commutator. When brushes which rest upon the 
slip rings are connected with a source of alternating current 
of proper voltage, the armature will rotate as a motor and the 
current intake will 
be sufficient to sup- 
ply the direct-cur- 
rent circuit and to 
overcome losses in 
the converter due 
to resistance, fric- 
tion, hysteresis and 
eddy currents. The 
windings of a con- 
verter armature are 
closed, like those of 
a direct-current 
generator armature, 
and each slip ring is 
connected , to the 
armature winding 
by as many taps as 
there are pairs of 
field poles. 




433. — Winding of a Rotary Converter 
Armature for a Bipolar Field. 

The taps are shown for single-, two- and three-phase 
operation. 



The proper taps for single-, two- or three-phase currents from 
a ring-wound armature placed in a bipolar field are shown in 
Fig. 433, the ring-wound armature and the bipolar field being 
used in order to simplify the explanation. In practice rotary 
converters have multipolar field frames and drum-wound arma- 
tures, but their operation is practically the same as that of the 
machine represented in Fig. 433. 

If the converter represented by the armature in Fig. 433 is to 
operate on single-phase alternating current, the current is lead 
to and from the winding through taps 1 and 7, which taps would 
be connected to two slip rings; for two-phase operation two 
more rings would be added to the machine and connected to 



544 



LESSONS IN PRACTICAL ELECTRICITY 



the taps 4 and 10, thus making four sHp rings and four brushes 
on the alternating-current side of the machine. If the armature 
were to be used on a three-phase circuit it would be provided 
with three slip-rings that would connect to the taps 1, 5 and 9 
respectively. In any of these cases, whether the machine 
operates from a single-phase or polyphase circuit, a direct- 
current pressure can be obtained at the brushes A and B. 
The continuous E. M. F. bears a fixed ratio to the impressed 
alternating E. M. F. and will be equal to the maximum alter- 




Fig. 434. — Three-phase Synchronous Converter. 

nating E. M. F.; therefore, the value of the direct pressure 
obtained from a single-phase rotary would be equal to the 
effective value of the impressed alternating E. M. F. times 
1.41. For polyphase converters the ratio of conversion will 
depend upon the number of phases and the method of connect- 
ing the windings, for example, in a two-phase rotary the ratio 
of the alternating to the direct E. M. F. for each phase is 0.71, 
and in a three-phase rotary this ratio is 0.62 for each phase. 
Rotary converters are mostly of the polyphase type; a three- 
phase rotary is shown in Fig. 434. 

Rotary converters may be started and be brought up to 
synchronous speed by the same methods that are employed 



ALTERNATING-CURRENT APPARATUS '545 

with synchronous motors, ^ 374. They may also be started 
from the direct-current side when direct current is available, 
by operating the machine as a direct-current shunt motor and, 
after shutting off the direct-current, applying the alternating 
current through the low-voltage taps of an auto-transformer, 
the voltage being increased until the machine is in synchronism. 
If a direct current is supplied to a rotary converter through the 
brushes and commutator it will run as a shunt motor while 
alternating current may be taken from the slip rings; under 
these conditions the machine is termed an inverted converter. 

Rotary converters of large capacity or those that may be 
required to carry large momentary overloads have commu- 
tating poles, which fulfill the same functions as they do in 
direct-current generators and motors, ^ 296, that is, insuring 
sparkless commutation from no load to heavy loads with a 
fixed brush position. Machines of this type that are started 
from the alternating-current side are provided with a mechani- 
cal brush-raising device, for the brushes must be raised from 
the commutator in order to prevent sparking. Another use 
that is made of the commutating poles in rotary converters is to 
provide regulation of the ratio between the voltages of the 
direct-current side and the alternating-current side by varying 
the excitation of the commutating poles w^ith a field rheostat 
that is inserted in series with the pole windings; converters 
having this form of regulation are termed regulating-pole rotary 
converters. 

367. Rectifiers. — To change small amounts of alternating 
current to direct current, a cheaper device than the rotary 
converter or motor-generator set is used, and is termed a 
rectifier. There are four types in use, namely: the mercury arc 
rectifier, the vibrating rectifier, the tungar rectifier and an 
electrolytic rectifier. 

Mercury Arc Rectifier. — The essential part of the mercury 
arc rectifier is a glass bulb of the shape shown in Fig. 435, 
exhausted of air and containing only mercury vapor. The tube 
has four terminals passing through the glass and connecting 
with iron or graphite electrodes, the two lower electrodes 
1 and 4 being covered by pools of mercury. This device is a 
valve in that it permits current to flow only from a positive 



546 



LESSONS IN PRACTICAL ELECTRICITY 



terminal to the pool of mercury; thus current may flow from 
either electrodes 2 or 3 to the mercury pool 1, but not in the 
reverse direction. A bulb of this nature would cease to operate 
on alternating-current voltage after half a cycle if some means 
were not provided to maintain a flow continuously toward the 

negative electrode. The 

y^ufo -Transformer tWO auodes, 2 and 3, 

Tlnnnnnnn/innn/)oJ_J ^ connected to each side 

of the transformer are 
also connected through 
reactances L and Li to 
one side of the battery 
B, and the cathode, 1, is 
connected to the other 
side of the battery. The 
small starting electrode, 
4, is connected through 
a resistance to one side 
of the alternating-cur- 
rent circuit, and, by tilt- 
ing the tube so the mer- 
cury bridges the space 
between electrodes 1 
and 4, an arc forms as 
the tube is brought 
back to its vertical 
working position, thus 
starting the operation 
of the rectifier bulb. If 
at that instant the ter- 
minal T of the trans- 
former is positive, the 
anode 2 will be positive, and the current will pass from 2 to 1, 
then down through battery B, through reactance coil L and 
back to the negative terminal Ti of the transformer, as shown by 
arrows not inclosed in circles. When the alternating E. M. F. 
falls, before it reaches a value insufficient to maintain the 
arc, the reactance L comes into play and keeps the current 
flowing for a short time in the same direction as formerly. 




Mercury Arc Rectifier. 



ALTERNATING-CURRENT APPARATUS 



547 



To Alfernaiing-Curreni Line 

wmmm 



Primcrry 



Transformer 



Secondary 



This serves to maintain the arc in the rectifier bulb until the 
voltage of the .alternating-current supply has passed through 
zero, reverses and builds up such a value as to cause the anode 3 
to have a sufficiently positive value to start the arc between it 
and the cathode 1. The discharge circuit of the reactance 
L in the meanwhile 
is through the arc be- 
tween 3 and 1 instead 
of through its former 
circuit, and the direct 
current down through 
the battery con- 
tinues. The arc be- 
tween 3 and 1 is later 
supphed with current 
from the transformer 
since terminal Ti is 
then positive ; the 
circuit is indicated by 
the arrows inclosed 
in circles. 

To obtain the cor- 
rect voltage for the 
battery B which is 
being charged, the 
auto- transformer 
from which current 
is derived is tapped 
at the proper point 
by the aid of a dial 
switch, S. The ordi- 




Circuits of a Vibrating Rectifier. 



nary form of this type of rectifier used for charging vehicle 
batteries has a maximum capacity of 30 amperes. 

Vibrating Rectifier. — The vibrating rectifier is a mechanical 
device for changing an alternating current to a direct current. 
Its chief use is for charging three-cell storage batteries, such as 
are used on automobiles or for gas engine ignition, from an 
alternating-current lighting circuit. The rectifier consists of a 
transformer to reduce the voltage of the lighting circuit to the 



548 LESSONS IN PRACTICAL ELECTRICITY 

proper value, and an electrically-operated switching mechanism 
to rectify this reduced voltage. In this rectifier, the circuits of 
which are shown in Fig. 436, the transformer is used, not only 
to reduce the voltage, but also to provide a neutral or return 
path for the direct current. The load current flows from one 
end of the secondary winding of the transformer, through the 
regulating resistance, R, through one pair of contacts, C, 
which are automatically closed at the proper time, and out 
from the center point of the vibrating armature to the battery 
under charge, from which it returns to the central point, or 
neutral, of the transformer. During the succeeding half cycle, 
when the voltage of the transformer secondary is reversed in 
direction, the other pair of contacts is closed and voltage is 
applied to the battery from the half of the secondary previ- 
ously idle, this voltage being in the same direction as during 
the preceding half cycle. The important part of the rectifier, 
and upon which its successful operation depends, is the vibrating 
mechanism which reverses the connections in synchronism and 
in step with the reversal of voltage so as to open the current- 
carrying circuit at the instant of zero current and thus prevent 
sparking and injurious wear of the contacts. The vibrating 
part of the apparatus consists essentially of a polarized relay 
acted upon by two alternating-current magnets so that it 
vibrates in synchronism with the alternations of the current. 
The vibrating arm is magnetized by a current shunted from the 
battery, so that one end is permanently north and the other 
end permanently south, depending on which way the battery is 
connected. The two alternating-current magnets are stationary 
and wound so that their lower ends are of the same polarity 
at each instant. When the alternating current flows in one 
direction, the lower poles of both stationary magnets will be 
north, consequently attracting the south end of the vibrating 
arm and repelling the north end, which causes one set of con- 
tacts to close. As the current reverses both lower poles of 
the stationary magnets will become south, thus attracting the 
north end of the vibrating arm and closing the other set of con- 
tacts. This reverses the connection of the alternating-current 
to the direct-current circuit, but as the direction of current has 
also reversed, the current flows into the direct-current circuit 



ALTERNATING-CURRENT APPARATUS 



549 



in the same direction as before. The reversal of connections 
thus takes place every time the current reverses, so that the 
result is a pulsating direct current. 

An adjustable resistance, Fig. 436, is connected in series 
with the alternating-current magnets to secure exact timing 
for the breaking of the current-carrying circuit at the instant 
when the battery and transformer voltages are equal and oppo- 
site and no current is flowing, thus insuring sparkless operation. 
The adjustable resistance alters the power factor of the magnet 
circuit without affecting that of the 
transformer circuit, and this change 
in power factor translates in time 
the impelling force with respect to 
the current in the contacts and al- 
most secures sparkless operation. 
To reduce to a negligible amount 
the unavoidable slight sparking, due 
to the fluctuations in line voltage, 
variation in wave form and change 
in battery voltage, condensers are 
connected around the contacts. 

An external view of a type G vi- 
brating rectifier made by the West- 
inghouse Electric & Manufacturing 
Company is illustrated in Fig. 437; 
the upper terminals are provided 
with an attachment plug for connection to an ordinary lamp 
socket supplied with alternating current; the lower terminals are 
the connections to the storage batter}^ It is immaterial which 
of the two direct-current leads is connected to the positive or 
negative side of the batterj^ The standardization of lighting 
batteries in general use has resulted in the selection for the 
commercial form of this apparatus of such transformer voltage 
and resistance values as to make the charging current under nor- 
mal conditions approximately 8 amperes at the start of charge 
and 6 amperes at the finish. 

The Tungar Rectifier. — A vacuum tube containing a hot 
and a cold electrode acts as a rectifier, and this principle is 
utilized in the Tungar rectifier bulb. Fig. 438. The bulb con- 




Fig. 437. — Westinghouse 
Vibrating Rectifier. 



550 



LESSONS IN PRACTICAL ELECTRICITY 




Fig. 438. — Tungar 
Bulb. 



tains an inert gas at low pressure, a filament of small tungsten 
wire coiled into a closely wound spiral, and a piece of graphite 
of relatively large area, the graphite serving as the anode and 
the tungsten filament as the cathode. The inert gas in the 
bulb is ionized by the negative charges of elec- 
tricity or electrons which are emitted from the 
incandescent filament, and the ionized gas acts 
as the principal current carrier and is capable 
of passing a current of several amperes, the 
current being limited by the design and size of 
the bulb. During one half cycle, when the 
incandescent tungsten filament is negative, 
the electrons emitted from it are being at- 
tracted toward the anode by the voltage 
across the bulb, these electrons colliding with 
the gas molecules and ionizing them, that is, 
making them conductive in the direction of 
anode to cathode; while during the other half 
cycle, when the filament is positive, any elec- 
trons that are emitted are driven back to the filament, so that 
the gas is non-conductive during that half cycle; consequently 
the bulb rectifies only one half 
the alternating-current wave. 

The connections of a half- 
wave Tungar rectifier are shown, 
in Fig. 439, the apparatus con- 
sisting of the bulb B, with fila- 
ment (catho,d&)'C and anode A, 
the transformer T for furnish- 
ing current to the filament, the 
rheostat R, and the storage bat- 
tery. Assuming an instant when 
terminal 1 of the alternating- 
current supply is positive, the current flows in the direction of 
the arrows through the battery, rheostat, bulb and back to the 
opposite terminal 2 of the alternating-current line. When ter- 
minal 2 becomes positive no current flow takes place, for the 
current is permitted to flow only from the anode to the cathode, 
or against the flow of emitted electrons from the cathode, 




Fig. 439. — Circuit of Half-wave 
Tungar Rectifier. 



ALTERNATING-CURRENT APPARATUS 



551 




Fig. 440. — General Electric Co. 
Tungar Rectifier. 

Six-ampere 75-volt size. 



but it cannot flow from the cathode to the anode. To rectify- 
both half-waves would require two bulbs properly connected. 
The general principles just 
described apply equally well 
to the half -wave and full-wave 
types of rectifi.ers. The half- 
wave rectifiers are particu- 
larly applicable to low-cur- 
rent, low-wattage designs, on 
account of -the much lower 
cost of manufacture and 
lower cost of bulb renewals. 
Commercial types of this 
form of rectifier, one type of 
which is shown in Fig. 440, 
are made in the following 
sizes for operation on 115- 
volt, 60-cycle alternating-cur- 
rent circuits: a 2-ampere, 7.5- volt unit for charging small three- 
cell batteries at 2 amperes ; a 6- 
ampere, 7.5-15-volt unit, for 
charging three or six cells of bat- 
tery at 6 amperes; a 6-ampere, 
7. 5-75 -volt unit for charging from 
three to thirty cells of battery at 
from 1 to 6 amperes. 

Electrolytic Rectifier. — To ob- 
tain relatively small amounts of 
direct-current power from alter- 
nating-current circuits, use is 
made of the fact that certain 
metals when immersed in certain 
electrolytes offer a high resis- 
tance to the passage of an electric 
current in one direction and a low 
resistance if the current flows in 
the other direction. For commer- 
cial use a cell consisting of a plate 
of aluminum and a plate of lead inamersed in a solution of am- 




Trans former 



/WVWWVWWV 

, 1' A/ww^__il 




L^^^_!_^^ 



Fig. 441. — Connections of a 4- 
cell Electrolytic Rectifier. 



552 LESSONS IN PRACTICAL ELECTRICITY 

monium phosphate has been found to give the best results. 
The action when alternating current is sent through the cell is 
the formation of a film of hydroxide of aluminum over the sur- 
face of the aluminum plate, which offers a high resistance to the 
current when it flows from the aluminum to the lead through 
the solution, but offers very little resistance when flowing in the 
opposite direction, resulting in a suppression of half of the 
alternating wave, and producing pulsating current in one 
direction only. 

Both halves of the alternating waves are utilized by an 
arrangement of four cells connected as in Fig. 441. A trans- 
former is generally used as shown to reduce the line voltage to 
the lower voltages needed for battery charging purposes and 
the exact amount of resistance is regulated by the resistance R. 
The current will flow during one alternation from terminal 1 of 
the transformer through cell 1, battery B to point C and then 
through cell 3, to terminal 2 of the transformer; during the 
next alternation the current will flow from terminal 2 through 
cell 2, battery B to point C and then through cell 4 to ter- 
minal 1. It will be noted that the current always flows through 
the cells from the lead plate to the aluminum plate, as very 
little current can flow from the aluminum plate to the lead; 
therefore, the current always flows from point A and it is to 
this point that the positive terminal of the storage battery 
must be connected to tiave the charging current flow through 
the battery in the proper direction. To obtain the best effi- 
ciency with the above apparatus the electrolyte should be kept 
at a temperature not exceeding 70° Fahrenheit. 

QUESTIONS 

1. What is the function of a transformer and what does it consist of? 

2. Name three types of transformer construction and give several 
methods used for coohng transformers. 

3. Describe the action of a transformer with a load on the secondary. 

4. How would you determine the efficiency of a transformer? 

5. What are the two general types of construction used for alternators? 

6. What are the advantages of a revolving-field alternator over one of 
the revolving-armature type? 

7. Is the three-phase alternator armature of Fig. 430 A- or Y- 
connected? 



ALTERNATING-CURRENT APPARATUS 553 

8. What are rotary converters and for what purpose are they used? 

9. What is the difference between a rotary converter and a motor- 
generator set? 

10. What is a rectifier; name four different types? 

11. Make a sketch of the mercury arc rectifier circuits and describe 
the action of this type of rectifier. 

12. Describe the Tungar rectifier. 



PROBLEMS 

1. What is the frequency of an alternator having 30 poles and revolv- 
ing at 240 revolutions per minute? Ans. 60 cycles. 

2. What are the full-load currents in the two windings of a 20-kw. 
transformer that is used to supply electricity to a number of 110-volt 
lamps? The primary voltage is 2200 volts, ratio of the transformation is 20, 
and the efficiency of the transformer is 97 per cent. Ans. 9.09 amperes in 
primary; 181.8 amperes in secondary. 

3. (a) The copper and iron losses of a 25-kw. transformer are 400 
watts and 350 watts respectively when the transformer is delivering full 
load; what is its efficiency? (6) If the secondary voltage at full non- 
inductive load is 112 volts, what should be the voltage at the primary if 
the ratio of transformation is 10? Ans. (a) 97 per cent, (b) 1156 volts. 

4. Electrical energy of 1100 kw. is to be delivered at 2200 volts from 
secondaries of transformers located in a sub-station situated 25 miles from 
a hydro-electric generating plant. Efficiency of the step-down trans- 
formers in the sub-station is 98 per cent, ratio of transformation is 10. (a) 
What is the voltage at the primaries of the step-down transformers? (5) 
What is the voltage at the secondaries of the transformers located in the 
generating station if there is a voltage drop of 10 per cent on the transmis- 
sion line? (c) What power is delivered to the secondaries of the trans- 
formers in the generating station? (d) What would be the circular mil area 
of the wire required to effect the transmission? Ans. (a) 22,450 volts; 
(h) 24,950 volts; (c) 1248 kw.; {d) 57,000 circular mils. 



LESSON XXX 

ALTERNATING-CURRENT MOTORS 

Polyphase Induction Motors — Squirrel-Cage and Wound Rotor Induction 
Motors — Starting of Polyphase Induction Motors and Speed Control 

— Single-Phase Induction Motors — Single-Phase Commutator Motors 

— Synchronous Motors — Starting of Synchronous Motors — Motor- 
Generator Sets — Questions. 

368. Poljrphase Induction Motors. — There are four general 
types of alternating-current motors: 

1. Polyphase induction motors, 

2. Single-phase induction motors, 

3. Single-phase commutator repulsion motors, 

4. Synchronous motors. 

The polyphase induction motors of the squirrel-cage arma- 
ture type is the simplest and most common form for industrial 
use. The induction motor may be compared with a direct- 
current shunt motor in that it has two parts: the stationary 
part corresponding to the direct-current motor field is called 
the stator and the rotating member that corresponds to the 
armature of the direct-current motor is called the rotor, 
the essentipJ difference being that the armature or working 
current of the direct-current motor is led into it by brushes, 
while the working current of the induction motor is an induced 
or '' transformer '' current in the rotor windings produced by 
the alternating field set up by the currents flowing in the 
stator windings. The induction motor thus combines the 
principles of a motor and a transformer, rotation being pro- 
duced by the revolving member following a rotating magnetic 
field, which is the resultant of two or more alternating mag- 
netic fields set up by the polyphase currents flowing through 
the stator windings. The speed of rotation of the field is given 

554 



ALTERNATING-CURRENT MOTORS 555 

by the following equation which is derived from Formula (120) 
by transposition 

120 X frequency. /i>ic\ 

rev. per mm. = i — -^, .... (14bj. 

number ot poles 

this is known as the synchronous speed of the induction motor. 

As a simple illustration of the principle of a rotating magnetic 
field, imagine a horseshoe magnet to be held over a compass 
The needle will immediately take up a position parallel to the 
magnetic flux passing from one pole of the magnet to the other, 
and it is perfectly obvious that if the magnet is rotated the 
compass needle will follow. A rotating magnetic field can also 
be produced by polyphase currents flowing through two or 
more groups of coils wound on inwardly projecting poles of a 
circular iron ring, the coils on each group of poles being wound 
alternately in opposite directions and connected to a single 
E. M. F. This action will be explained by the aid of Fig. 442, 
which shows a four-pole field ring energized by two windings 
connected separately with the two phases of an alternator. 
The direction of the magnetic field will be indicated by a 
magnetic needle which will always move to a position where 
it will be parallel with the magnetic flux passing from pole to 
pole. If the current in one set of coils is increasing while the 
current in the other set of coils is decreasing, the needle will 
be attracted toward the poles in whose coils the current is in- 
creasing until that current reaches its maximum value. At the 
bottom of Fig. 442 is shown the phase relation of the two 
sinusoidal E. M. F.'s which are applied to the two windings of 
the four-pole ring, phase 1 supplying current to the coils on 
poles A and Ai and phase 2 supplying current to the coils on 
poles B and Bi. 

In Fig. 442, at I, the current of phase 1 is at a maximum 
and the poles of coils AAi are fully magnetized, while the poles 
of BBi are not magnetized since the current of phase 2 is zero 
at the instant shown; consequently the magnetic needle (or a 
bar of iron may be used) will assume the vertical position shown. 
At the instant shown at II, the current in coils AAi (phase 1) 
has decreased to the same value ' as that to which the cur- 
rent in coils BBi (phase 2) has increased and the four poles 



556 



LESSONS IN PRACTICAL ELECTRICITY 



are now equally magnetized as shown, drawing the needle to 
the position indicated. At the instant shown at III, the cur- 
rent of phase 1, connected to coils AAi, has decreased to zero, 




I 

Phase 1 at maximum current 
PhoiseZat izvo current. 




Phase 1 at zero current 
Phase 2 at maximum current 




y^---Phase2'-- 

. n 

Phase I with decreasina 
current. Phase 2 with 
increasing current. 



^ 


"Nu 


J^ 


■^ -o 


,x^ 


\ / 


> 


r 


\^ 


X 


$/ 


/ 


\ 


X'o 


/ 


/ 


\ 


\ vO 


/ 


1 . 


v 


\ 




/Time / 


A 






\l/ 


u 



I I I 



Fig. 442. — Production of a Rotating Magnetic Field by Two-phase j 

Currents. . j 

while the current of phase 2, connected to coils BBi, has reached ' 

a maximum. The magnetism of coils BBi draws the needle | 

into a horizontal position. The above action is repeated during ! 

successive instants of the flow of the alternating currents and \ 



ALTERNATING-CURRENT MOTORS 



557 



the needle continues to revolve in the same direction within 
the field frame as long as the two-phase currents are supplied 
to the two sets of coils. If the compass needle be replaced by 
an iron core wound with copper conductors, secondary currents 
will be induced in these conductors producing a magnetic field 
which will react on the rotating magnetic field and cause rota- 
tion of the iron core (the 
rotor), just as the compass 
needle of Fig. 442 revolved 
with the rotating field. 
The rotating magnetic field 
exerts a pull or drag upon 
the rotor which causes it 
to revolve with the field. 

The torque exerted by 
the rotor in a field frame 
constructed with project- 
ing poles, as in Fig. 442, 
would not be uniform, as 
the magnetic flux from 
instant to instant in such 
a field would be irregular 
and the attraction or drag 
on the rotor pulsating in 
effect. Commercial polyphase induction motors have multi- 
polar field frames without such projecting poles. The laminated 
core of the stator of induction motors is built up of thin iron 
or steel plates having slots in which the windings are imbedded, 
the stator. Fig. 443, resembling the stationary armature of a 
revolving-field alternator. The coils of the stator winding are 
distributed symmetrically over the entire face of the core and 
connected to form distinct groups which overlap each other. 
The windings are formed into two circuits for a two-phase 
motor and into three circuits for a three-phase motor, and these 
circuits are supplied with current respectively from a two- or 
three-phase alternator. 

Fig. 444 shows diagrammatically the arrangement of a two- 
phase stator, in which the A coils connect to one phase and the 
B coils to the other phase of a two-phase circuit. Starting 




Fig. 443. — Stator of Polyphase 
Induction Motor. 



558 



LESSONS IN PRACTICAL ELECTRICITY 



with instant I when the current in coils A is at its maximum 
value, and consequently the magnetizing force of this set of 
coils at its maximum, the current and magnetizing force of 
circuit B will be at zero value. Four poles, alternating N and S 
around the core, are formed directly under coils A. As the cur- 
rent in circuit A begins to decrease, that in B rises, and the mag- 
netizing forces of the two overlapping windings will act together 
at some points and are opposed at others, making the resultant 
magnetic field shift to one side of the former position. As the 
current in circuit A gradually falls to zero and that in circuit B 
rises to its maximum value the magnetic field shifts around 




Fig. 444. — Progressively Shifting Magnetic Field Produced in a Multi- 
polar Field Ring with Two-phase Currents. 

until it is directly under coils B. If the current in circuit A 
should next increase in the same direction as before, while 
that in circuit B diminished, the magnetic poles would shift 
back again to their former position. But after reaching zero 
value, the current in circuit A rises in the opposite direction, 
while that in B falls. This shifts the resultant poles forward 
instead of backward, and they gradually shift ahead until they 
are again directly under coils A. But the N poles now occupy 
the former position of the S poles. Thus, with the current in 
circuit A passing from a maximum in one direction to a maxi- 
mum in the opposite direction, the poles have shifted forward 
the width of one polar space. Current in circuit B next rises 
in a reversed direction and the poles shift forward until, when 
the current in B is a maximum, they are under coils B. The 
diagrams I, II, III of Fig. 444 show the positions of the shift- 



ALTERNATING-CURRENT MOTORS 



559 



ing field under certain conditions of current in the two circuits. 
In II the position shown is an arbitrary one, for it depends upon 
the relative values of the currents in the two circuits. With the 
two currents equal, the position of the line N-N would be half- 
way between coils A and B. 

369. Squirrel-Cage and Wound Rotor Induction Motors. — 
Squirrel-Cage Rotors. — The rotor or armature of a squirrel- 
cage type induction motor is shown in Fig. 445, and consists 
of a laminated steel core having slots that are parallel with the 
rotor axis in which copper bars are imbedded. The bars are 
connected in parallel to 
copper collars placed one 
at each end of the rotor ; 
these are termed end 
rings. The current in- 
duced in the copper con- 
ductors flows in a direc- 
tion parallel with the 
rotor axis and the reac- 
tion of the magnetic flux 
of these rotor conductors 
against the rotating field 
is therefore in a proper direction to produce rotation. The 
speed at which the rotor revolves is always less than that of the 
revolving field, for if the rotor revolved at the same speed as 
the rotating field there would be no cutting of the rotor con- 
ductors by the field, hence no induced current in the rotor con- 
ductors nor reactions on the rotating field to produce mechani- 
cal power by the rotor. The ratio of the difference in speed of 
the rotor and the rotating field to the speed of the rotating 
field is known as the '' slip " and is usually expressed as a per- 
centage. As the load on the motor is increased the speed of 
the rotor decreases almost in proportion to the load over a 
certain range; the maximima speed would then occur when the 
motor is running with no load. 

The polyphase induction motor with squirrel-cage rotor has 
the advantages of being simple and rugged in construction, 
self-starting under load, exerting a powerful torque, and hav- 
ing a practically constant speed at all loads. This type of 




Fig. 445. — Rotor of Squirrel-cage Motor. 



560 



LESSONS IN PRACTICAL ELECTRICITY 



motor is particularly suitable in places where there is inflam- 
mable material, as the motor requires no collector rings and 

brushes from which sparks 
are liable to arise. Fig. 446 
shows an assembled poly- 
phase induction motor. 

In order to reverse the 
direction of rotation of a 
polyphase induction motor 
it is necessary to reverse 
the direction of rotation of 
the field, which is accom- 
phshed by reversing the flow 
of current in only one of the 
phases. By referring to 
Fig. 442, it can be seen that 
if the connections to one of 
the phases had been re- 
versed the field would have 




Fig. 446. — Squirrel-cage Induction 
Motor Complete. 



revolved in the opposite direction. 

Wound Rotors. — A type of rotor frequently used in large 
induction motors has polar windings similar to the winding 
on the stator. In one type the rotor windings are short-circuited 




Fig. 447. — Wound Rotor of Induction Motor. 



through an adjustable resistance carried on the rotor spider, , 
the resistance being gradually cut out of circuit as the motor " i 
speeds up by pushing a knob on the end of rotor shaft; the \ 
motor at full speed operates as a squirrel-cage motor, with \ 
short-circuited winding. The maximum torque which an indue- ., 
tion motor can exert is found to be the same for different rotor 1 



ALTERNATING-CURRENT MOTORS 561 

resistances, but the speeds when exerting this maximum torque 
are different. A high rotor resistance means that the torque 
will be large at low speeds and that the current will be rela- 
tively small. Therefore resistance is inserted in the rotor wind- 
ing at starting of the motor in order to insure a small starting 
current under load and a high starting torque. 

In another type of wound rotor, Fig. 447, the winding ter- 
minals are brought out to slip rings, and the starting resistance, 
which is external to the motor, is connected with the rotor 
windings by means of brushes rubbing upon the slip rings. 
When the motor reaches its proper speed, the resistance is 
gradually cut out so that a large torque is secured within the 
operating speed range. 

370. Starting of Polyphase Induction Motors and Speed 
Control. — If the stator windings of an induction motor, whose 
rotor is at rest, be connected directly to the supply circuit 
they would draw large currents, for exactly the same condition 
arises as when the primary of a transformer, whose secondary 
is short-circuited, is connected directly to the supply circuit. 
These starting currents in the induction motor become less as 
the rotor acquires speed. 

Induction motors, say up to 5 H. P., may be connected directly 
to the supply line through fuses and a switch, but the momen- 
tary rush of current at the start may be two to five times that 
of the full-loa_d current and consequently a fuse that would 
protect a motor from an injurious overload would be blown 
whenever the motor is started. This condition necessitates a 
special arrangement of fuses for such sized motors which are 
not equipped with a starting device. This arrangement employs 
two sets of fuses, one set having a current-carrying capacity that 
would accommodate the starting current without blowing, and 
the other set of fuses having a lower capacity sufficient to 
carry the full-load current of the motor; in case of an overload 
on the motor the latter fuses will be blown and protect the 
motor. Such an arrangement of fuses and a double-throw 
switch is shown in Fig. 448. The switch is thrown down to 
start the motor, thus connecting it directly to the line through 
the starting fuses, then, when the motor has gained nearly full 
speed, the switch is quickly thrown up, thus putting the run- 



562 



LESSONS IN PRACTICAL ELECTRICITY 



Line 



fSfariing fuses 




Fig. 448. — Connections of 
Two Sets of Fuses for Starting 
Small Induction Motors. 



ning fuses in series with the motor. Automatic starters may 
also be used with small motors; they consist of double-pole 
switches which are magnetically operated. 

The method of starting squirrel-cage induction motors hav- 
ing an output of 5 H. P. and over is to reduce the line voltage 

applied to the motor at starting; 
the voltage is reduced through an 
auto-transformer termed a starting 
compensator or auto-starter. The 
p. -. p, ,. ^ ^ ^nij.uunc^ auto-starter first connects the 

U D U T T T^''""^^ motor to the Hne through the auto- 

transformer so that the voltage is 
reduced and the current drawn 
from the line kept within moderate 
limits ; naturally the starting torque 
is also reduced. After the rotor 
has increased sufficiently in speed 
the motor terminals are connected 
directly across the line. An exter- 
nal view of an auto-starter is shown 
in Fig. 449. The iron case contains several 
auto-transformers, each auto-transformer con- 
sisting of a single coil wound on a laminated 
iron core and having several taps brought out 
from the winding. When the auto-starters 
are shipped from the factory the starter ter- 
minals are connected to taps that give about 
65 per cent of the line voltage for starting, but 
extra taps from the auto-transformer are pro- 
vided inside the case, so that either 50 or 80 
per cent of the line voltage can be obtained 
if desired. 

The auto-starter is provided with an oil- 
immersed switch having two sets of butt con- 
tacts that close against coiled springs, one 
set of contacts being used for starting and the other for run- 
ning. The switch is operated by the handle on the front of 
the starter, see Fig. 449, and the construction is such that 
the handle must be moved to the starting position before it 




Fig. 449. — Auto- 
starter. 



ALTERNATING-CURRENT MOTORS 



563 



can be moved to the running position so that improper opera- 
tion is practically impossible. When the handle is moved to the 
starting position, those contacts are closed which connect the 
motor to the reduced Hne voltage derived through the auto- 
transformer, and when placed in the running position the other 
set of contacts are closed, connecting the motor directly to the 
full voltage of the line. The 
connection of an auto- 
starter for a three-phase 
motor is shown in Fig. 450. 
Another method of start- 
ing induction motors is by 
inserting resistance in the 
rotor circuit, this method 
being applicable only to 
motors having wound rotors. 
This resistance may be 
mounted directly on the 
shaft inside the rotor and 
controlled by a switch on 
the rotor shaft, as explained 
in ^ 369. With the slip- 
ring type of induction 
motor having a wound rotor, 
the starting resistance is ex- 
ternal to the motor and in 
the form of a '^starting box," 
somewhat similar to that for 



Running 
5ide 

Oil Swifch 

Star Unci 
Side 




Bac/< Finger 
Block 



Fronf Finger 
Block 

Auto 
Trans former 



Fig. 450. — Connections of a Three- 
phasa Auto-starter. 



a direct-current motor, there being a variable non-inductive re- 
sistance coil for each rotor circuit. Fig. 451 shows the internal 
connections of a rheostat for a three-phase slip-ring motor, the 
resistance coils for the three phases being simultaneously con= 
trolled by the three rheostat arms which are rigidly connected 
together. To start the motor the stator windings are connected 
to a three-phase supply circuit and the rheostat handle is moved 
in a direction to decrease the resistance in the three rotor circuits; 
when the rheostat arms have been moved to the limit of their 
motion all resistance has been cut out and the rotor winding 
short-circuited, the motor having reached its full speed. 



564 



LESSONS IN PRACTICAL ELECTRICITY 



To Slip Rirx^s 



The foregoing method of varying the amount of resistance in 
the rotor circuit is also used when it is desired to vary the 
speed of an induction motor over a small range; if the resist- 
ance of the rotor circuit is increased the rotor current is de- 
creased and the speed drops in order that the former rotor 

current value may be restored, re- 
sulting in inefficient operation of 
the motor. The speed of an induc- 
tion motor can also be varied by 
altering the voltage applied to the 
stator windings, or altering the 
number of rotating poles by com- 
mutating the stator windings. If 
the voltage applied to the stator is 
reduced the capacity of the motor 
is reduced since the capacity varies 
as the square of the impressed 
voltage. Altering the number of 
rotating poles requires an external 
switching device by means of which 
the polar grouping can be readily 




Fig. 45L — Starting Resist- ^ ^ ^ ^ 

ance for a Three-phase Slip- \x.^^„r,A \^(. p-iVf. fhp Hp^irpd ^vn 
ring Induction Motor. cnangea to give tne aesirea syn- 

chronous speeds; such a motor is 
called a multi-speed induction motor. Among the other schemes 
of speed control used are: cascade control, dynamic control, 
and brush-shifting motors. 

371. Single-Phase Induction Motors. — The single-phase 
induction ' motor differs from the polyphase type principally 
in the character of its magnetic field, as an ordinary single- 
phase winding will not produce a rotating field, but a field 
that is oscillating, and the induced currents and poles pro- 
duced in the rotor by this field will tend to produce equal 
torque in opposite directions, therefore, the rotor cannot start 
to revolve. However, if the rotor can in some manner be made 
to rotate at a speed corresponding to the frequency of the cur- 
rent in the stator windings, see Formula 146, U 368, then the 
reaction of the stator and rotor flux is such as to produce a 
torque that will keep the rotor revolving. 

In practice the starting of single-phase induction motors is 



ALTERNATING-CURRENT MOTORS 565 

accomplished by three general methods applicable to small- 
sized motors only. First: the split-phase method, in which an 
auxiliary stator winding is provided for starting purposes only, 
this winding being displaced from the main stator winding by 90 
electrical degrees. It has a higher inductance than .the main 
stator winding, thus causing the current in it to lag far enough 
behind the current in the main winding to produce a shifting 
or rotating field during the starting period, which exerts a 
starting torque on the rotor sufficient to cause rotation. When 
nearly normal speed has been reached the auxiliary winding is 
cut out of circuit by a switch and clutch in the motor, which 
operates automatically by centrifugal force, and the motor 
continues to run as a single-phase motor. The starting torque 
of such motors being limited, they are frequently constructed 
with the rotor arranged to revolve freely on the shaft at start- 
ing until nearly normal speed is reached, at which time the 
load is picked up by the automatic action of a centrifugal clutch. 

Second : an auxiliary winding may be connected to the single- 
phase line through an external inductance and a switch (for dis- 
connecting the auxiliary winding from the circuit after the motor 
has reached normal speed), the introduction of the inductance 
in the auxiliary winding splitting the phase as before. 

An ordinary polyphase induction motor may be operated on a 
single-phase circuit by splitting the single-phase in a manner 
similar to the above. If a two-phase motor has its two stator 
windings connected in parallel to a single-phase fine but with 
as much reactance as possible in series with one of the stator 
windings, while resistance is placed in series with the other, the 
current in one winding will be considerably out of phase with 
the current in the other, and a non-uniform rotating field will 
be produced. The squirrel-cage rotor will revolve in such a 
field but it will not develop the same amount of power as with a 
perfect rotating field. 

One of the stator windings may be disconnected from the 
circuit after the motor has attained normal speed, the motor 
then operating as a single-phase motor. Single-phase motors 
operated on the above principle are manufactured by the Gen- 
eral Electric Company; the stator of this type of motor has 
symmetrical three-phase windings which may readily be re- 



566 



LESSONS IN PRACTICAL ELECTRICITY 



connected for operations on three-phase circuits. When oper- 
ated on a single-phase circuit, the stator windings are connected 
to it through a resistance and reactance at starting by means 
of a starting box similar in appearance to the direct-current 

motor starting box. The rotor in 
this type of motor revolves freely on 
the shaft until about 75 per cent of 
normal speed is reached when the 
load is picked up by the action of a 
centrifugal clutch. 

Third : a single-phase motor having 
a wound rotor equipped with a com- 
mutator may be started as a repulsion 
motor, II 372, and when normal speed 
is attained, a centrifugal device auto- 
matically short-circuits the commuta- 
tor and at the same time lifts off the 
brushes, thus changing the machine 
to a single-phase induction motor. 

372. Single-phase Commutator 
Motors. — Single-phase motors pro- 
vided with commutators are of three 
general types, namely: plain repul- 
sion, single-phase series, and repul- 
sion-induction motor. 
In the plain repulsion motor, a rotor ex- 




Fig. 452. — Diagram of Two- 
pole Repulsion Motor. 



Repulsion Motor 
actly like a direct-current armature is placed in a magnetic field 
excited by an alternating current flowing through an ordinary 
single-phase stator winding. To secure the necessary torque the 
armature remains short-circuited in a line at a predetermined 
angle with the stator field flux, this being accomplished through 
brushes which rest on the commutator and are joined by a low- 
resistance connector. The pulsating flux produced by the alter- 
nating current flowing in the stator winding may be considered 
to have two components, one in the direction of the brush axis 
and the other perpendicular to this axis. The former compo- 
nent produces an electromotive force in the armature conductors 
and sets up a current in them, while the latter flux component 
reacts upon this armature current to develop torque. It is 



ALTERNATING-CURRENT MOTORS 567 

necessary, therefore, that the brush axis be located on a hne 
inclined at an angle to the axis of the field. Fig. 452 shows a 
simple diagram of the stator and rotor windings and the posi- 
tion of short-circuiting brushes for a two-pole repulsion motor. 
The operating characteristics of the plain repulsion motor have 
been improved by the use of a second set of brushes connected 
with a compensating field winding. 

Single-phase Series Motor. — The series motor for operation 
on single-phase alternating-current circuits is about the simplest 
form of a single-phase commutator motor, and in general design 
is practically the same as a direct-current series motor except 
that all the iron used for the magnetic circuit must be lami- 
nated and a neutralizing or compensating field winding is very 
often used. Since the direction of rotation of a direct-current 
series motor remains unchanged if the current through it is 
reversed at its terminals, H 284, it follows that any direct- 
current series motor will operate on alternating current. The 
armature of the series motor revolving in the alternating mag- 
netic fiux, will have several E. M. F.'s set up in its windings, as 
follows: first, an E. M. F. is induced in the armature by the 
periodic reversals of the flux from the field magnets; this is 
really a transformer action as this E. M. F. would be set up 
even if the armature was held stationary. Second, an E. M. F. 
is generated in the armature coils as they cut the flux when the 
armature rotates. Third, a reactive E. M. F. is set up in both 
the armature and field circuits due to their self-induction. The 
impressed E. M. F. must be high enough to overcome this 
reactive pressure and also the pressure generated by. the rotat- 
ing armature conductors in cutting the flux, this latter pressure 
being the same as the counter E. M. F. in a direct-current 
motor. Hence, the impressed alternating pressure must be 
greater than would be applied to a corresponding direct-current 
motor in order to overcome the above opposing pressures, and 
produce .a current equal to that produced by the direct-current 
pressure. The inductive action of the armature and field 
windings causes the current to lag considerably behind the 
impressed E. M. F., thus resulting in a very low power factor. 
Further, an analysis of this motor shows that it has a starting 
torque but little greater than the torque at normal speed, 



568 



LESSONS IN PRACTICAL ELECTRICITY 



Field 



Compen- 

saiing 

Winding 



s/r 







In order to improve the power factor and starting torque of 
the series motor some means must be taken to neutralize the 
armature reactive E. M. F., which is not essential to the 
operation of the motor. This neutralization is accomplished 

by the use of a compensating field 
winding, having such number of turns 
as to set up a magnetic field equal 
and opposite to that due to the cur- 
rent in the armature coils. The com- 
pensating winding may be energized 
by either one of two methods, the 
conductive or forced compensation, A, 
Fig. 453, in which the winding is con- 
nected in series with the main field 
winding and armature, or the induc- 
tive compensation, B, Fig. 453, in 
which is utilized the induced current 
obtained by short-circuiting the com- 
pensating winding upon itself. The 
latter method could. of course only be 
used when the motor operates on 
alternating current, while the former 
method can be used with either 
alternating or direct current. 

The objectionable sparking at the 
Fig. 453. — Connections of brushes of single-phase series motors 
Compensated Single-phase is caused by the local currents pro- 
Series Motor. (luced by the E. M. F. induced in the 
B-inSt^ItoZ'^iSiS^r- armature coils which are short-cir- 
cuited by the brushes, due to the 
periodic reversals of the field flux. The spark occurs as the 
short-circuit is opened when the commutator bars, to which the 
short-circuited coil is connected, leaves the brushes. This 
sparking is minimized by constructing the armature of many 
coils of but a few turns each, thus reducing the E. M= F. in- 
duced in each coil, and by the use of resistance leads between 
the armature conductors and the commutator segments. 

Compensated series motors are well adapted for traction 
service for they exert a large torque at starting and less torque 




ALTERNATING-CURRENT MOTORS 



569 




at high speeds. They have come into quite considerable use 
for operating large locomotives and interurban cars; in several 
installations the motors are operated over some parts of the 
road with direct current. 

An important commercial application of the principle of the 
series commutator motor is to be found in the construction of 
a small-size motor that will operate on either alternating or 
direct current, and for this reason termed a '' universal " 
motor. This ^' universal " 
motor is widely used for 
operating vacuum cleaners, 
fans, electric drills and other 
small electrical appliances. 

Repulsion-Induction Mo- 
tor. — The greatest applica- 
tion of the repulsion motor 
principle has been to im- 
prove the starting perform- 
ance of the ordinary single- 
phase induction motor, and 
the compensating-winding 
feature of the repulsion mo- 
tor is also often embodied in the single-phase repulsion-induc- 
tion motor. A motor of this type, made by the General Elec- 
tric Company, is shown in Fig. 454. The stator field consists of 
slotted laminations wound with two windings, a main winding 
and the compensating winding. The rotor is built of sheet steel 
laminations and its winding is the same as that on the armature 
of a direct-current series motor. The connections of the motor 
are shown in Fig. 455. These motors have four terminal leads 
brought out from the stator windings, permitting of the operation 
of the motor on either 110-volt or 220- volt circuits. By connect- 
ing adjacent pairs of these terminals in multiple, A to C and B 
to D, the motor can be operated on a 110-volt circuit, and by 
connecting terminals B and C together the two stator windings 
are connected in series and the motor can be operated on 220 
volts. The compensating field winding, C, which is auxihary 
to the main winding, is connected with a set of brushes termed 
the compensating brushes (5 and 7) and placed 90 electrical 



Fig. 454, — Single-phase Repulsion- 
induction Motor — General Electric Co., 
Type RI. 



570 



LESSONS IN PRACTICAL ELECTRICITY 



degrees from the main short-circuiting brushes; the latter 
brushes are referred to as energy brushes (3 and 4) and have 
about the same angular relations to the stator field as have 
the brushes of a plain repulsion motor. 

The compensating field which derives its current from the 
induced E. M. F. in the armature serves to correct the phase 
relation between the motor current and the voltage, thus pro- 
ducing high power factor at all loads. The compensating field 



220-VQlf SQrvicQ 




Fig. 455. — Connections of Type RI Four-pole 
General Electric Single-phase Motors. 



also serves to restrict the maximum no-load speed and to lessen 
the variation of speed which usually accompanies changes of 
load. This type of compensated repulsion-induction motor 
possesses heavy starting torque at all loads, and after starting, 
operates practically as an induction motor. It may be wound 
for speeds above or below synchronous speed at standard fre- 
quencies. The speed of these motors may be made variable by 
inserting an adjustable resistance, in the form of a rheostat, 
in series with brushes 3 and 4, which are normally short- 
circuited. 

Another type of compensated repulsion-induction motor, made 
by the Wagner Electric Manufacturing Company and known as 
type BK, has a rotor with two windings, a squirrel-cage wind- 



ALTERNATING-CURRENT MOTORS 



571 



Compensafinq 
Field; 



ing consisting of copper bars placed in the bottom of the rotor 
slots, and above these bars, a regular direct-current armature 
winding connected with the commutator on which four brushes 
rest. The connections of the main and compensating stator 
windings with the brushes and line are shown in Fig. 456. The 
motor is provided with a centrifugal switch, S, which keeps the 
compensating winding open-circuited during the starting of 
the motor but places it 
in series with the main 
stator windirigwhen the 
motor has acquired the 
proper speed. In opera- 
tion, the squirrel-cage 
winding does practically 
all the work, very little 
of the load current being 
carried by the brushes 
and commutator. The 
amount of compensa- 
tion can be varied by 
the lead L; when con- 
nected to point 7 maxi- 
mum compensation is 
obtained, thus giving a 
leading current at light 
loads; with L connected 
to 8, normal compensa- 
tion is secured, which gives nearly unity power factor at rated 
load. The particular advantages of this type of motor are: 
good power factor at all loads, practically constant speed at all 
loads, and a starting torque of approximately twice the full- 
load torque with the motor taking about three times full-load 
current. 

A type of repulsion-induction motor without compensating 
winding, also made by the Wagner Electric Manufacturing 
Company, has a stator with a single winding and a rotor pro- 
vided with form-wound coils the same as those of a direct- 
current motor armature. The carbon brushes, resting on the 
commutator during the starting of the motor, are all connected 




Fig. 456. — Connections of a Wagner 
Type BK Single-phase Motor. 



572 LESSONS IN PRACTICAL ELECTRICITY 

electrically by a low-resistance conductor, thus short-circuiting 
the armature winding. The brushes are adjusted to such posi- 
tions relative to the magnetic poles of the field, that a repulsive 
force is produced between these poles and the rotor poles, and 
the motor starts as a repulsion motor, the induced current in the 
rotor winding traveling the paths formed by the brushes. 
When the rotor has attained nearly normal speed, the brushes 
are no longer required and they are lifted from the commu- 
tator by a centrifugal device, while at the same time a ring of 
copper segments is forced into an annular opening in the com- 
mutator so as to short-circuit the entire rotor winding, thus 
transforming the rotor winding to the squirrel-cage form. The 
induced currents now traverse the individual^ coils of the rotor 
and the motor operates as a straight single-phase induction 
motor. It has practically constant speed, and will start under 
full load with a current about 1.5 times the full-load current. 

373. Synchronous Motors. — Any single or polyphase alter- 
nator will run as a motor if it is connected to a source of alter- 
nating E. M. F. of the same frequency and pressure as it 
produces as a generator, provided it is first brought to its 
synchronous speed before the E. M. F. is applied. The term 
synchronous means in unison, or in step ; so the rotor of a 
synchronous motor must revolve in unison, or in step, with the 
frequency of the alternating current supplied to it. For 
example, a synchronous motor having 24 poles and supplied 
with a 60-cycle current would run at a speed of 5 revolutions 
per second or 300 rev. per min., and when the motor has this 
speed it is said to be running in synchronism. This speed was 
obtained by dividing the frequency by the number of pairs of 
poles, Formula (146). 

It has been stated that any alternator may be run as a syn- 
chronous motor; therefore such a motor is constructed in 
practically the same manner as the corresponding alternator in 
that it has a field excited from a separate source of direct 
current and an armature, either of which may revolve, requir- 
ing in addition, however, some means to bring the rotating 
member up to synchronous speed before the motor is connected 
to the alternating E. M. F. 

The operation of the synchronous motor is due to the reaction 



ALTERNATING-CURRENT MOTORS 573 

between a magnetic field of a fixed polarity produced by a 
direct current, and a field of constantly changing polarity set 
up by an alternating current, the revolving part running at a 
speed that will keep the magnetic poles of a fixed N and S 
polarity close to each changing pole of the proper opposite 
polarity that will produce a pull for rotation of the rotor al- 
ways in one direction. If the simple form of alternator, shown 
in Fig. 308, has its armature coil connected to an alternating 
current that flows during one alternation in the direction from 
A to B, magnetic poles are produced in the armature loop that 
will be attracted by the oppositely-named poles of the field 
magnets; this attraction will tend to turn the armature in a 
direction opposite to that indicated by the arrow of rotation in 
Fig. 308. Before this magnetic attraction overcomes the inertia 
of the armature, the current through the loop will have been 
reversed and also its magnetic poles, thus tending to turn the 
armature in the opposite direction, that is, in the direction 
indicated by the arrow in Fig. 308. The alternations in the 
current occur with such frequency that the magnetic force in 
either direction does not persist long enough to produce rota- 
tion of the armature, with the result that it remains at rest, 
or it will simply vibrate. If, however, the motor armature is 
first brought to a speed corresponding with the frequency of the 
alternating current on which the motor is to be operated, then 
it will continue to revolve, because at synchronous speed the 
magnetic flux of field and armature are always in the same 
relative position. 

The single-phase synchronous motor has no starting torque, 
whereas the polyphase type when operated without load is self- 
starting, as there is always some turning effort exerted on the 
rotor due to the fact that as the current in the stator coils of 
one phase reaches zero the current is increasing in the coils of the 
other phase or phases, resulting in a revolving field around 
the surface of the armature. With the field circuit open, this 
rotary fiux sets up eddy-currents in the pole faces and reacts 
with them to develop torque. To aid the starting of polyphase 
synchronous motors, the polar faces of the rotating field have 
copper bars imbedded in parallel slots in the rotor core, the 
bars being connected to end rings forming an auxiliary cage 



574 LESSONS IN PRACTICAL ELECTRICITY 

winding similar to the rotor winding of a squirrel-cage induc- 
tion motor. A rotor constructed in this manner is shown in 
Fig. 457. With a rotor so constructed the motor will start, 
leaving the direct-current field circuit open, by applying the 
alternating pressure to the stator or armature windings. 

Another advantage of the cage winding on the rotor is that it 
acts as a damper to prevent " hunting " of the motor. The 




Fig. 457. — Rotor for Self-starting Synchronous Motor. 

term '' hunting " as apphed to synchronous motors means the 
periodic fluctuations in rotor speed, or the periodic surging of 
current between the motor and the alternator supplying the 
current. If, due to a sudden increase in load, the rotor is 
slightly retarded, the armature will take more current from the 
line and will accelerate the rotor so as to shift the phase of its 
" counter " E. M. F. in respect to the impressed ^. M. F. 
It will shift it too much, however, and the driving torque will 
be lessened until it is rendered insufficient for the motor load, 
whereupon the rotor will again lag, and so on. This oscillation 
of the rotor about its mean speed, that is hunting, is effectively 
reduced by the damping coils or cage of the rotor. • 

The use of synchronous motors is limited to large capacities 
where starting under load is not necessary, for the following 
reasons: the difficulty of starting, the small starting torque, 
and the fact that a direct current is required for the field excita- 
tion. Where it is possible to use induction motors, synchronous 



ALTERNATING-CURRENT MOTORS 



575 



motors are seldom used as they require more care than the 
induction type. The chief advantages of the synchronous 
motor are: its constant speed at all loads, and the power factor 
can at all times be controlled by varying the field strength. 
The current can be made to lead the impressed E. M. F. by 
this change of excitation, which fact is utilized in neutralizing 
the lagging current taken by induction motors that may be con- 
nected to the same circuit as the synchronous motor. Synchro- 
nous motors are frequently connected in transmission lines for 
the purpose of regulating their phase relations, the motor being 
run without load and the field excitation increased to suit the 
conditions. In such cases, where the synchronous motor oper- 
ates only to correct power factor, it is termed a synchronous 
condenser, for the reason that its action on a circuit is the same 
as that of a condenser, K 355. 

374. Starting of Sjmchronous Motors. — Synchronous motors 
do not have sufficient starting torque to come up to speed under 
load, and therefore 

require an auxiliary lamp-, 

source of power, such 
as an induction mo- 
tor, to bring them 
up to synchronous 
speed. Thereafter, 
the electromotive 
force induced in its 
winding must have a 
phase difference of 
about 180° with the 
impressed voltage 
before the motor can 
be connected to the mains. A device, known as a synchronizer, 
is used to determine these two points. The simplest form of 
synchronizer consists of incandescent lamps connected across 
a switch inserted in the circuit of the motor to the supply cir- 
cuit as shown in Fig. 458. The lamps will be brightest when 
the phase difference between the service and motor E. M. F.'s 
is zero, and will be .dark when the phase difference is 180°, the 
lamps being alternately bright and dark as the motor comes up 




A.Cl/ne 



Lamp. 
Fig. 458. — Synchronizing by Means of Lamps. 




576 LESSONS IN PRACTICAL ELECTRICITY 

to synchronism. When synchronism is approached, the altera- 
tions in the brilUancy of the lamps become slower and finally 
become so slow as to permit closing of the main switch at an in- 
stant when the lamps are dark. 

Instead of the lamps, an instrmnent known as a synchro- 
scope, Fig. 459, is extensively used to determine when syn- 
chronism has been reached. The 
instrument is provided with a pointer 
which rotates at a speed propor- 
tional to the difference in frequency 
between the E. M. F. of the motor 
and that of the supply service to 
which the motor is being synchro- 
nized. When the machine is in syn- 
chronism and the pointer comes to 
rest at the top of the scale, the main 

Fig. 459.^S^chroscope. ^"^'^f "^"^y ^"^ '''"f ^' ^'^"^ connect- 

mg the motor to the supply circuit. 

Synchronous motors whose rotors are constructed with the 
self-starting auxiliary winding are started as induction motors 
with reduced pressure through the use of auto-starters similar 
to that shown in Fig. 449, the direct-current field circuit being 
open at starting. When the motor has reached nearly syn- 
chronous speed the full alternating pressure is applied to the 
stator winding and also the direct current to the revolving 
field windings. When starting in this manner precaution must 
be taken against the puncturing of the insulation of the field 
coils, due to the high voltage produced in them by the alter- 
nating flux. This is accomplished by the use of a field break-up 
switch, which is a multi-blade switch connected in the field 
circuit, so that each field spool is open-circuited on starting, 
and is connected to the direct-current circuit as the motor 
reaches synchronism. 

375. Motor- Generator Sets. — The difference between a 
motor-generator set and a rotary converter is that the former 
consists of a motor mechanically coupled to one or more gen- 
erators, with all machines usually mounted on the same bed 
plate; while the rotary converter is a single machine perform- 
ing the functions of a motor and generator. In a motor- 



ALTERNATIN(>-CURRENT MOTORS 



577 



generator set of two machines, both may be designed for direct 
current or both for alternating current, or again, one may be for 
direct and the other for alternating current. A motor-generator 
set of the first type converts from a direct current at one volt- 
age to a direct current at another voltage, see If 322. The 
second type is used chiefly for converting alternating current 
of one frequency to that of a different frequency, with or with- 
out a change in the number of phases, or in the voltage. This 
type, known as a frequency changer, is used to interlink power 




Fig. 460. 



Motor-generator Set for Converting Alternating Current 
to Direct Current. 



systems of different frequencies. The third and largest class is 
employed, like rotary converters, to convert alternating current 
to direct current. 

The motor-generator sets of the third type are suitable for a 
large variety of uses, some of which are as follows: to obtain 
direct current for charging storage batteries, using the power 
furnished by alternating -current circuits, in connection with 
garages, railway signal systems, telephone circuits, etc.; to 
furnish direct-current for operating arc lights for stereopticon 
and motion picture outfits or similar work, where the flicker 
of alternating-current arcs is objectionable; and to furnish 
low- voltage direct currents for electrolytic work. 



578 LESSONS IN PRACTICAL ELECTRICITY 

The general appearance of motor-generator sets is indicated in 
Fig. 460. This illustration shows a General Electric 155-kw. 
set composed of a 2300-volt revolving-field synchronous motor 
{i.e., an alternator running as a motor) and a 250-volt direct- 
current compensated interpole generator. 



QUESTIONS 

1. Name four general types of alternating-current motors. 

2. How can a rotating magnetic field be produced? 

3. What are some of the advantages of the polyphase induction motor 
of the squirrel-cage type over a shunt-wound direct-current motor? 

4. What is the function of an auto-starter such as is used with poly- 
phase induction motors? 

5. How does a single-phase induction motor differ in operation from 
a polyphase induction motor? 

6. State three general methods used for the starting of single-phase 
induction motors. 

7. Name three general types of single-phase commutator ntotors; 
state briefly how they operate. 

8. What is a synchronous motor? 

9. To what use are synchronous motors limited? 

10. How are synchronous motors started and what means would you 
use to determine when the motor is running in synchronism? 



LESSON XXXI 
RADIO SIGNALING 

Electromagnetic Waves — Table XX — The Production of Electromag- 
netic Waves — Frequency, Oscillation Constant and Wave Length — 
Damped Waves and Continuous Waves — Types of Antennas — 
Methods of Exciting the Antenna Circuit — Table XXI — Continuous- 
Wave Transmission Systems — Radio Frequency and Audio Frequency 
— Radio Receiving Sets — Vacuum Tubes — The Vacuum Tube as a 
Detector and an Amplifier — The Vacuum Tube as an Oscillation- 
Generator or Oscillator — How the Waves Leave the Transmitting 
Antenna — Loop Reception — Radio Direction Finder — Questions. 

376. Electromagnetic Waves. — Any alternating current 
causes the radiation in all directions of electromagnetic energy 
into space in the form of electromagnetic waves. In fact, any 
electrical disturbance, as for instance, a change in the current 
strength in a conductor, causes some radiation of electro- 
magnetic energy. By making the frequency of an alternating 
current very great as compared with the frequencies commonly 
employed in electric lighting and power circuits, it is possible 
to radiate electromagnetic energy in all directions, and for 
great distances, from the conductor carrying this high-frequency 
current, although the radiation may be greater in some direc- 
tions than in others. It is possible to detect the presence of this 
energy by means of suitable apparatus affected by it and 
remotely situated from the source of energy. 

This simple principle of the radiation of electromagnetic 
energy through space and the detection of its presence forms 
the basic principle employed in systems of radio telegraphy and 
radio telephony. In simple systems of radio telegraphy, the 
radiation of electromagnetic energy into space from the trans- 
mitting station is controlled by means of a telegraph key in the 
usual manner so as to form dots and dashes. The International 
Code is used universally. In systems of radio telephony, 
energy continuously is radiated from the transmitting station 

579 



580 



LESSONS IN PRACTICAL ELECTRICITY 



while speaking. The effect of the voice in the telephone trans- 
mitter is to vary or modulate the radiation of energy, in the 
form of electromagnetic waves, from the transmitting station, 
without changing the continuity nor the frequency of the waves. 
The propagation of electromagnetic energy through space is 
accompUshed through the hypothetical ether, regarding which 
little is known, but light, heat and other electromagnetic dis- 
turbances, in the form of electromagnetic waves, are propagated 
through it at the rate of 300,000,000 meters (approximately 




-One Alfernafion^ >j-s---C7/7e Alternoifion 

-180° ->[<- -180°- 

One Cycle - - 

Or?e Wave Lengf-h- 

Time orPeriocf- 

y^ , J0O°- 



Fig. 461. — Sine Wave of Alternating Current. 



186,500 miles) per second. The ether is assumed to occupy all 
space regardless of the presence of matter, since the particles 
constituting the structures of matter are very widely separated 
as compared with the space which they individually occupy. 
Any electric current produces in the ether interlinked magnetic 
and electrostatic fields at right angles to each other. When 
any alternating current is reversing, the magnetic and static 
fields reverse at the same instant and some of the energy is 
propagated through the ether at the rate of 300,000,000 meters 
per second. If the frequency of this current was 300,000,000 
cycles per second, the energy would travel only one meter by 
the time that one complete cycle had taken place, and one 



RADIO SIGNALING 581 

complete cycle constitutes one complete wave. Therefore, the 
wave length would be one meter with a frequency of 300,000,000 
cycles per second. 

Fig. 461 illustrates a sine wave form which is generally as- 
sumed in radio calculations; this is identical with that shown 
in Fig. 400. It has the general shape of water waves, but 
the electromagnetic waves radiated froni a radio transmitting 
station travel in all directions and, therefore, are greatly 
different from water waves which travel only in one plane. 
Electromagnetic waves travel through space whether or not 
this space is occupied by any other substance such as air, wood, 
etc., although not so well as through the ether alone, but they 
act on electric conductors in such a manner as to tend to pro- 
duce high-frequency alternating currents in such conductors. 
Hence, the energy of the electromagnetic waves may be con- 
verted into electric energy in such conductors, and this is the 
principle of the reception of radio signals. 

The phenomenon of light is a manifestation of the presence of 
electromagnetic waves of exceedingly high frequencies as com- 
pared with radio frequencies, yet light travels from the heated 
filament of an incandescent lamp through the vacuum (ether) 
between the filament and the glass bulb, through the glass 
and air surrounding it, and, impinging upon the optic nerve 
produces the sensation of light. The presence of the glass 
bulb and the air surrounding it is a detriment rather than a 
benefit, and these have no functions whatsoever in the propa- 
gation of the electromagnetic waves (called light waves in this 
case). In this illustration an incandescent lamp serves as a 
transmitter and the eye as a receiver. In fact, naval vessels 
are equipped with so-called '' blinkers " which operate on this 
principle, by using the International Code. 

Wave lengths corresponding to various radio frequencies are 
computed by dividing 300,000,000 meters per second (the 
velocity of propagation) by the frequencies in cycles per second, 

, ,, . , 300,000,000 meters per second ^, 

or wave length m meters = . : — . The 

frequency m cycles per second 

Greek letter X (lambda) is used to represent the wave length 
in meters; v the velocity of propagation, and f the frequency 



582 



LESSONS IN PRACTICAL ELECTRICITY 



in cycles per second. Therefore, the foregoing equation may | 

be written j 

X = - meters (147). j 

^ I 



and 



f = - cycles per second (148), 

A 



Table XX. Wave Lengths Corresponding to Various Frequencies 



Frequency in 


Wave length 


Frequency in 


Wave length 


cycles per second 


in meters 


cycles per second 


in meters 


300,000,000 


1 


300,000 


1,000 


30,000,000 


10 


100,000 


3,000 


3,000,000 


100 


50,000 


6,000 


1,000,000 


300 


30,000 


10,000 


500,000 


600 


20,000 


15,000 



In general, passenger steamships employ radio apparatus 
having wave lengths varying from 300 to 600 meters, while the 
wave lengths of some of the large land stations vary from 
1,000 to 15,000 meters. By tuning the circuits of radio receiv- 
ing sets it is possible to cause the radio receiving apparatus to 
respond only to a given wave length. Then, although there 
may be many stations sending messages at other wave lengths, 
practically no interference will result as all other wave lengths 
are " tuned out,^' unless the station receiving happens to be 
near a station transmitting, when interference will result through 
forced oscillations, due to the proximity of the two stations. 
Recently, interference has been termed jamming. 

377. The Production of Electromagnetic Waves. — The elec- 
tricity in a conductor is set in motion when acted upon by vary- 
ing magnetic fields, providing that the conditions are such that 
the electricity can move and thus form an electric current. 
An antenna may be considered broadly as a lightning rod,* 
cut apart near the ground, with radio apparatus connected 
therein. When an alternator is connected in series with a 

* Benjamin Franklin made the first receiving antenna, using his body- 
as a detector, in connection with the key attached to the moistened string 
leading to his kite, and making connection with the ground by standing 
upon it. 



RADIO SIGNALING 583 

lightning rod, or a modern antenna, the alternating E. M. F. 
alternately forces electricity up the rod or wire, away from the 
ground, and down the rod towards the ground. One side of 
the alternator is connected to the rod and the other side is con- 
nected to the ground. Therefore, there is a difference of 
potential between the ground and the rod or wire when an 
E. M. F. is impressed upon them by the alternator. Con- 
sequently, the wire and ground act like the opposite plates of 
a condenser (Fig. 286, ^ 264). 

All antenna circuits contain both inductance and capacitance 
(also called capacity, If 347). The inductance has a retarding 
effect on the motion of electricity, while capacitance tends to 
accelerate its motion. An analogy of capacitance is found in 
the timing fork used by musicians. Owing to the '' springiness " 
of the steel, the tuning fork always tends to maintain a fixed 
shape, but when a prong is struck a sharp blow it is displaced 
from its normal position and tends to instantly resume that 
position. However, the inertia of the prong prevents it from 
instantly flying back, but its velocity increases as the prong 
approaches its normal position, so that when the prong does 
reach that position, its velocity is a maximum. Then the inertia 
of the prong causes it to keep on going beyond its normal posi- 
tion, thus displacing it as before, but in the opposite direction. 
When the Idnetic energy (motional energy) is all converted 
into potential (static) energy, the prong starts towards its 
normal position again; and so it swings or oscillates to and fro 
until all of the energy has been radiated away in the form of 
sound waves, or has been converted into heat. Comparing 
this fork with an electric circuit, it appears that capacitance 
may be called the " electric springiness," and inductance the 
'' electric inertia " of a circuit. Through the combined effects 
of inductance and capacitance the electricity in an antenna is 
made to oscillate to and fro when given an " electric blow," 
as in short-wave spark sets, or when set into continuous oscilla- 
tion by some device like an alternator, operating in tune with 
the circuit; this oscillation causes electromagnetic waves to be 
radiated throughout space. 

378. Frequency, Oscillation Constant and Wave Length. ^ — 
The natural frequency of the oscillating circuit is increased 



584 LESSONS IN PRACTICAL ELECTRICITY 

when either the inductance or the capacitance is decreased, 
and vice versa. If either one of these constants be increased 
and the other decreased so that their product remains unchanged, 
then the frequency of the circuit will remain the same. These 
facts can be put in the form of an equation by letting L be the 
inductance in henrys (If 343) and C be the capacity or capaci- 
tance in farads (Ij 347) ; then the natural frequency in cycles 
per second is given by 

f = ^ , (149). 

27rVL X C 

where t = 3.1416, and where the square root of the product of 
the inductance and capacitance is called the oscillation constant. 
In radio practice the units of inductance and capacitance above 
mentioned are unduly large, and for convenience the millihenry * 
( = one-thousandth of a henry) and the microfarad ( = one- 
millionth of a farad) are used instead. With these units Formula 
(149) becomes rnoo 

f = ^^^^ (150). 

VLxC 

Problem 154. — The oscillation frequency of an antenna current is 
100,000 cycles per second. Find the oscillation constant. 

By Formula (149) VlC = —= — = 0.00000159. 

^ ^ 27rf 6.28x100,000 

The wave-length can be expressed in terms of the oscillation 

constant by equating Formula (148), namely 

_ V 300,000,000 

*"X" X 

with Equation (149) ; thus, 

300,000,000 1 



X 27rVLC 

whence 

X = 1,885,000,000 VlC meters (151). 

Transposing Formula (151), the oscillation constant becomes 

VLC= ^^ (152). 

1,885,000,000 

* The centimeter is another unit of inductance much used. One million 
centimeters equal one millihenry. 



RADIO SIGNALING 



585 



Problem 155. — The oscillation constant of a circuit is 0.000003183. 
Find the wave length. 

By Formula (151) X = 1,885,000,000 x 0.000003183 = 6000 meters. 

Problem 156. — An aerial has a capacity of 0.0012 microfarad. What 
should its inductance be in order to have a wave length of 600 meters? 

From Table XX (^ 376) the frequency is 500,000 cycles for a wave length 
of 600 meters; therefore from Formula (150) 

5033 



Then 

or, since C 



L xC 



= 0.01006. 
500,000 

0.01006 X 0.01006 



0.0001012 



0.0012 microfarad, 

. 0.0001012 



0.0012 



= 0.0843 millihenry' 



379. Damped Waves and Continuous Waves. — A damped- 
wave radio transmitting set behaves very much hke a tuning 
fork or a bell, only electromagnetic waves are radiated from it 







/ / 

Fig. 462. — Damped Wave Trains. 

Produced by spark radio sets. 

into space instead of sound waves into the air. A sharp " elec- 
trical blow " is struck, and then the electricity in the antenna 
circuit vibrates to and fro, or oscillates at the natural frequency 
of the circuit, and the energy of the blow is quickly dissi- 
pated, part being radiated away into space, and the remainder 
converted into heat in the antenna circuit due to its resistance 
(see PR loss, ^237). Therefore, if a series of ''electrical 
blows " is given the electricity in the antenna circuit in such 
an order of succession that a blow shall be struck just as the 
effect of the preceding blow dies out, a series of groups of con- 
stantly decreasing waves will result which can be represented 
graphically as in Fig. 462. Such a wave train is said to con- 
sist of damped waves. 



586 



LESSONS IN PRACTICAL ELECTRICITY 



On the other hand, if the antenna circuit is struck '' elec- 
trical blows " in such a rapid order of succession that the cir- 
cuit will continue to vibrate continuously and harmoniously, as 
when a high-frequency alternator supplies energy to the antenna 
circuit at the natural frequency of the antenna circuit, then an 




Fig. 463. — Undamped or Continuous Waves. 



" undamped " or continuous-wave train will result, as depicted 
in Fig. 463. Damped waves are characteristic of ^' spark '^ 
telegraph transmitting sets, while continuous waves are em- 
ployed in radio telephone transmitting sets, as well as in 
continuous-wave telegraph transmitting sets. 

380. Types of Antennas. — In this chapter, the term antenna 
will signify the entire radiating or receiving system. In Fig. 

464, the aerial is the wire, or group of 
wires connected in parallel, strung be- 
tween masts or other supports and 
insulated therefrom. The counter- 
poise may be a wire screen, like 
" chicken wire," or it may be similar 
to the aerial and is either suspended 
slightly above the ground, laid upon 
the ground, or may be the ground 



Inducfance ^ 
Coil 



Aerial 



Counterpoise 



Fig. 464. — Elements of a 
Radio Antenna. 



inductance , 
Co a 



i Condenser- 



itself if there is sufficient moisture to 

make the ground a good conductor. 

On ships, metal parts, such as a steel 

hull, form the counterpoise; in this 

case the water acts as part of the 

counterpoise. In airplanes, the aerial 

trails behind the airplane, and the 

engine, stays, etc., either collectively 

or individually, form the counterpoise. The greater part of the 

inductance of the antenna system is usually contained within 

the radio set itself. 



Fig. 465. — ^Electrical Equiv- 
alent of a Radio Antenna. 



RADIO SIGNALING 



587 



Asria/ 




The aerial and counterpoise, then, while possessing some 
inductance, really form the capacitance part of the antenna 
circuit and are the equivalents of the two plates of a condenser. 
Fig. 465 shows a cir- 
cuit with inductance jhsuiator 
and capacitance con- 
nected in series, and is 
the electrical equiva- 
lent of Fig. 464, with 
the exception that a 
condenser of small size 
is used instead of an 
aerial and counter- 
poise, although the capacitance of the former may be equal to 

that of the latter. 
When the circuit is 
struck an '^ electrical 
blow," an E.M.F. will 
be induced in it which 
will cause an electric 
current to oscillate 
therein, but the ar- 
rangement shown in 



Fig. 466. — L-type Aerial. 



.rfnsufafor 




Fig. 467. — T-type Aerial. 



-Insula for 



Fig. 464 will radiate electromagnetic waves to a comparatively 

great extent, while the compact arrangement shown in Fig. 

465 will radiate only 

over a restricted range. 

The condenser should 

be extended in size in 

order to obtain good 

radiation. 

The principal types 
of aerials are the '' L ", 
"T", ''V", and 
'' Umbrella " types. The reasons for these names will be ap- 
parent by referring to Figs. 466 to 469 inclusive. In all cases, 
the lead-in wire is the wire connecting the aerial with the 
inductance. All of these aerials, with the single exception of 
the umbrella type, possess what is known as the directional 




Fig. 468. — V-type Aerial. 



588 



LESSONS IN PRACTICAL ELECTRICITY 



effect, which means that energy is transmitted and received 
better in certain directions than in others. The umbrella type 
functions equally well in all directions, while, in the other 
types, the directional effect is best in the direction of the lead-in 
wire. Therefore, the apex of the '' V," for instance, always 
should be pointed towards the distant station in order to 
obtain the best results, although inferior communication can 
be obtained from all other directions. In the T-type antenna, 
equally good results can be obtained from directions at the right 
or left of the lead-in wire, when viewed as in Fig. 467. 

A general rule for the lengths of aerial wires, as measured 
from the lead-in wire connection, is to make them approximately 



,-!nsula-f-or 




Fig. 469. — Umbrella-type Aerial. 

I of the wave length for transmitting stations. In other words, 
the wave length will be approximately 4.5 times the length 
of the aerial wire. This makes the length of an aerial wire 
slightly less than a quarter wave length. For receiving stations, 
the length of the antenna usually is not so important a matter. 
Experience shows that there is a best wave length for trans- 
mission over any given distance, this is called the optimum wave 
length. 

All antennas possess natural wave lengths, owing to their in- 
ductances and capacitances. Some inductance always is added 
to the antenna circuit in order that the antenna may be tuned 
to a given wave length, or to a series of given wave lengths, 
and to provide means for coupling the aerial with the radio 
apparatus. The proper wave length for a transmitting antenna 
may be found bj^ exciting the antenna circuit and, with a hot- 
wire ammeter connected in the antenna circuit, adjusting the 



RADIO SIGNALING 



589 



Atrial 



Inducfcince 



Coun-terpoisK 
or Ground 



Alfernafor 




Fig. 470.— Dia- 
grammatic Rep- 
resentation of an 
Antenna Circuit. 



inductance until the maximum current strength is obtained. 
For a given input, the antenna is then radiating the maximum 
amount of energy. Sometimes there is also a 
condenser which can be connected in series with 
the antenna circuit for decreasing the wave 
length of the antenna; this is called a short- 
wave condenser. 

All parts of a transmitting antenna must be 
thoroughly insulated from each other and 
widely separated so that sparks cannot jirnip 
from one part to another. Since receiving an- 
tennas are subject to very slight electrical 
strains, the matter of insulation is not so im- 
portant excepting that precautions should be 
taken so that no leakage, as 
through water or moisture, 
will result. The lead-in and 
the ground or counterpoise 
wire should be widely separated to prevent 
capacitance effects and absorption. In many 
installations the same antenna is used for 
both transmitting and receiving purposes. 
In connection diagrams the antenna circuit 
will generally be represented as in Fig. 470. 

381. Methods of Exciting the Antenna 
Circuit. — There are two general methods- 
employed for exciting the antenna circuit, 
known as the direct, and the indirect excitation 
transmission systems. The simplest method 
of directly exciting the antenna circuit would 
be to connect the armature of a high-frequency 
alternator in series with the antenna circuit, 
as in Fig. 471. In such an arrangement, it 
would be necessary to run the alternator at 
such a constant speed that its frequency 
should be the same as the natural frequency of the antenna 
circuit. Such alternators are employed in some large radio 
stations. These machines are by no means simple alternators 
and must be run at very high speeds; however, they produce 



Fig. 471. — 
Direct Excita- 
tion of Antenna 
by a High-fre- 
quency Alterna- 
tor. 



590 



LESSONS IN PRACTICAL ELECTRICITY 



He/ix 



Transformer 



continuous waves and, therefore, cause the radiation of the 
maximum amount of energy. 

In the ordinary syarli sets, the antenna is alternately excited, 
or struck an " electrical blow," and then left to oscillate at its 
natural frequency, thus producing damped waves since the 
resistance of the antenna circuit causes the conversion of some 
of the energy into heat. A simple representation of this method 
is illustrated in Fig. 472. With the alternator constantly run- 
ning, when the key is depressed an alternating current with a 

frequency of, say, 500 cycles 
per second, flows through the 
primary of a transformer which 
raises the E. M. F. up to, say, 
20,000 volts (maximum value 
of wave) on the secondary side. 
This E. M. F. is sufficient to 
break down or puncture the 
air in the spark gap 1000 times 
per second, since the E. M. F. 
reaches its maximum value 
during each alternation, or 
twice per cycle. When a spark 
passes, the secondary of the 
transformer is practically 
short-circuited owing to the 
fairly good conducting path of 
the spark, and the antenna then oscillates at its natural frequency 
of thousands of cycles per second for each time that the gap 
has been broken down by the 500-cycle E. M. F. The energy 
is quickly damped out after each break down due to the radia- 
tion of energy in the form of electromagnetic waves, the heat 
developed in the spark, and the heat developed in the wires of 
the antenna circuit, before the exciting E. M. F. of the trans- 
former again attains its maximum. The radiated waves during 
each breakdown make up one wave train. Fig. 473 shows the 
relation between the low-frequency E. M. F. in the secondary of 
the transformer which produces the sparks, and the high-fre- 
quency current in the antenna circuit. There is an antenna cur- 
rent only during the periods that the gap is bridged by a spark. 




Fig. 472. 



- Elements of a Spark 
Radio Set. 



RADIO SIGNALING 



591 



The logarithmic decrement is a measure of the time rate of 
decay of damped waves. Its value is expressed by the logarithm 
(to base e = 2.718) of the ratio of two successive amplitudes 
of the wave train in the same direction; the logarithmic decre- 
ment is given by the equation 



d = loge 



(153). 



where a and b are two successive amplitudes of the wave train. 




Current 



Fig. 473. — Production of Oscillations by Spark Sets. 

The antenna current has a much greater frequency than the 
current in the transformer that excites the antenna. 

This can be expressed in terms of ordinary logarithms (^^ 
base 10) by the formula 



8 



2.303 log,, ^ (154). 

b 



In 1912 the U.S. Government, in order to limit the inter- 
ference of radio stations with each other, adopted a law 
which, among other provisions, required that the logarithmic 
decrement of the waves radiated from a transmitter shall not 
exceed 0.2. 



592 



LESSONS IN PRACTICAL ELECTRICITY 



The significance of logarithms is briefly as follows: Ten squared is 
10 X 10 = 100, and therefore 100 is said to be the second power of 10; like- 
wise 1000 is the third power of 10 and, of course, 10 is the first power of 10. 
In the same manner any number may be considered as being a power of 
ten. The numbers lying between 10 and 100 will be somewhere between 
the first and second powers of ten. Those numbers between 100 and 1000 
will be more than the second power of ten and less than the third power. 
Tables have been prepared that show the power of ten which will raise 
it to any given number. Thus 10^ equals 10; whence the logarithm of 10 
to the base 10 is 1. Similarly, the logarithm of 100 is 2, and the logarithm 
of 1000 is 3. The logarithm of 45 is greater than 1 and less than 2; from 
a table of logarithms, its value is found to be 1.653, or 10^-^^^ equals 45. This 
system of logarithms which uses 10 for a base is called the common or Briggs 
system of logarithms; a short table of these logarithms is given in Table 
XXI. 

It is not necessary to use 10 as the base of logarithms; any number 
may be chosen as the base for a system, 3 for example. With 3 as a base, 
the logarithm of 9 would be 2, log 27 would be 3, log 81 would be 4, and 
so on, for 9 is the second power of 3, 27 is the third power of 3, and 81 is 
the fourth power of 3. The base of the so-called natural or Napierian 
system of logarithms is 2.718. In other words, all numbers instead of 
being considered as certain powers of 10 as in the common system of 
logarithms are represented as powers of 2.718; this number is frequently 
referred to as e (epsilon). 

Table XXI. Logarithms to Base 10 



1.0 





5 


0.699 


13 


1.114 


45 


1.653 


1.1 


0.041 


6 


0.778 


14 


1.146 


50 


1.699 


1.2 


0.079 


7 


0.845^ 


15 


1.176 


55 


1.740 


1.4 


0.146 


8 


0.903 


20 


1.301 


60 


1.778 


1.7 


0.230 


9 


0.954 


25 


1.398 


70 


1.845 


2.0 


0.361 


10 


1.000 


30 


1.477 


80 


1.903 


3.0 


0.477 


11 


1.041 


35 


1.544 


90 


1.954 


4.0 


0.602 


12 


1.079 


40 


1.602 


100 


2.000 



Problem 157. — The successive amplitudes of a damped wave train are 
10, 9.0, 8.1, 7.3, etc. Find the logarithmic decrement of the waves. 



10 1.11,^0 = 1.11,^ 
'8.1 '7.3 



1.11; 



The ratio of two successive amplitudes is — 

thus - has the constant value of 1.11. 
b 

The logarithm to base 10 of 1.11 is approximately 0.041, therefore the 
logarithmic decrement from Formula (154) is 5 = 2.303 logio 1.11= 2.303 x 
0.041 = 0.094. 



RADIO SIGNALING 593 

The resistance, inductance and capacity all affect the loga- 
rithmic decrement, as given by the formula 



TrRy/; 



(155). 



This formula is strictly applicable only to those circuits which 
are non-radiative, but if R represents the total resistance of 
the antenna circuit, ohmic and radiation resistance, the formula 
is accurate. From this formula, it will be seen that the greater 
the resistance and capacity of a circuit and the less the in- 
ductance, the greater will be the damping or the decrement of 
the circuit. In order, then, to produce feeble damping of the 
current in the antenna circuit and hence feeble damping of 
the electrical waves which it radiates, there should be a high 
inductance in the circuit and low values of resistance and 
capacity. 

Before the spark occurs, energy from the transformer is 
stored between the aerial and the counterpoise, or ground; 
these acting like the two plates of a condenser. When the 
E. M. F. becomes so great that a spark passes, due to elec- 
tricity being forced across the spark gap, this energy is released 
and the electricity oscillates at a high frequency to and fro 
across the spark gap and through thehelix of wire in the antenna 
circuit which is coiled to produce sufficient inductance in a 
compact manner. The capacitance of the antenna, between the 
aerial and the counterpoise, and the , inductance of the helix 
determine the wave length of the antenna. In some spark 
transmission systems, an induction coil (^ 263) is used instead 
of an alternator and transformer, and is operated from a direct- 
current circuit. The methods above described are all direct 
excitation transmission systems. 

In indirect excitation transmission systems, there is no spark 
gap in the antenna circuit, but the spark gap is placed in an 
oscillating circuit coupled with the antenna circuit, as in Fig. 
474. The coupling is accomplished by means of a high-fre- 
quency or oscillation transformer, which consists of two helices 
or inductance coils placed one inside the other, or end to end. 
When the latter consists of one continuous coil used as a trans- 



594 



LESSONS IN PRACTICAL ELECTRICITY 



former, it is called an auto-transformer, If 357. High-frequency 
inductance coils and transformers have air cores. 

Two circuits are said to be coupled when energy from one 
circuit can be transferred to the other circuit. For instance, an 
oscillating circuit containing an inductance coil may be coupled 
with an antenna in which another inductance coil is inserted, 
by placing the coils, one over the other, or end to end, so that 
the varying magnetic flux developed by the oscillating current 
in one of the inductance coils shall interlink with the turns 
of wire in the inductance coil of the other circuit. The ratio 
between the E. M. F. induced in one of the coils and the time 




Fig. 474. — Coupled-circuit Spark Set. 

rate of change in the current strength in the other coil (which 
produces the varying magnetic flux to induce the above E. M. F.) 
is called the mutual inductance of the two coils. Two circuits are 
said to be loose-coupled when the mutual inductance is of low 
value, as when the coils are not very near to each other, and 
close-coupled when the mutual inductance is relatively great. 
Sharp tuning is obtained with loose coupling. 

In the direct excitation transmission system shown in Fig. 472, 
the oscillations are damped by the resistance of the spark. 
In the indirect excitation transmission system shown in Fig. 474, 
there is not so much damping in the antenna circuit on account 
of its low resistance, and the oscillations continue in the antenna 
circuit after the spark has ceased in the tuned coupled circuit. 
In indirect excitation transmission systems, it is important that 
the product of the inductance and capacitance in the antenna 



RADIO SIGNALING 



595 



circuit and the product of the inductance and capacitance in the 
coupled oscillating circuit shall be equal, as then the circuits 
are in tune with each other, both having the same wave length, 
or period. 

A quenched spark is one which is quickly extinguished after 
it has ^' struck." In connection with the indirect excitation 



Primary 



Secondary 



fHi k ' ^ - '^ ' 



a/\/\M^\/w 



I y^lll/v AiyiA- aAAA ' ai\n^ ""Vw - 



Fig. 475. — Transfer of Energy in Coupled Circuits. 

The curves show the currents in the primary and secondary wind- 
ings of the oscillation transformer. When the current in one coil 
oscillates over its maximum range, the current in the other coil almost 
ceases. 

transmission, a quenched spark has the advantage of giving 
the antenna circuit (through the coupled circuit) a sharp 
" electrical blow." and then permitting the electricity in the 



Primary 




Secondary 



Fig. 476. — Oscillations in the Gap and Antenna 
Circuits of a Quenched-gap Transmitter. 

The current in the primary or gap circuit is highly damped; 
this permits the antenna or secondary circuit to radiate its energy 
with feeble damping. 

antenna circuit to freely oscillate at the natural frequency of the 
antenna circuit without transferring energy from the antenna 
circuit through the coupling back to the oscillation circuit, 
which results when the spark is not quickly extinguished. A 
quenched spark gap consists of a number of metal disks insu- 
lated from each other by means of mica washers, thus forming 



596 LESSONS IN PRACTICAL ELECTRICITY 

a chain of short spark gaps connected in series, and with suffi- 
cient masses of metal to prevent detrimental heating which 
would encourage the ionization of gases and prolong the dura- 
tion of the spark. Some spark gaps are water-cooled in order 
that the spark may be more quickly extinguished. A similar 
effect is approximated by the use of a toothed wheel which, 
running in synchronism with the alternator, permits a spark 
to pass only when a tooth is opposite the stationary electrode 
of the spark gap. 

Fig. 475 illustrates how energy is transferred from the 
coupled oscillating circuit to the antenna circuit and then back 
from the antenna circuit to the coupled oscillating circuit, etc., 
as when " long " or " ordinary " spark gaps are used, while 
Fig. 476 shows the effect of a quenched, or " short," spark in 
acting only long enough to get the electricity in the antenna 
circuit oscillating properly, and then to cease altogether so as 
not to interfere with the oscillations in the antenna circuit. 

382. Continuous- Wave Transmission Systems. — Continu- 
ous electric oscillations are produced by high-frequency alter- 
nators, electric arcs, and vacuum tubes. The alternator method 
has been touched upon in the last paragraph in connection with 
Fig. 471. If the key is held down, the alternator will produce 
continuous electric oscillations of equal amplitude in the 
antenna circuit, and a continuous-wave train will be radiated 
into space. 

An arc transmission system is illustrated in Fig. 477. The 
electric arc is operated by a direct-current generator with a 
choke coil (much inductance) and a resistance connected in 
series. When the current strength in the arc increases, the 
voltage across the arc decreases, and vice versa. When the cur- 
rent first begins to flow through the arc, the condenser in the 
oscillating circuit at the left in Fig. 477 is charged and, being 
connected in shunt with the arc, diverts some current from the 
arc, which causes the E. M. F. across the arc to increase and 
thus further charge the condenser, until the E. M. F. of the 
condenser is equal to that of the arc. However, the inductance 
in series with the condenser in the oscillating circuit possesses 
the property of " electric inertia," so that the electricity keeps 
on flowing and charges the condenser to a higher E. M. F. 



RADIO SIGNALING 597 

than that of the arc. Then the condenser commences to dis- 
charge through the arc, in the opposite direction, much as it 
would discharge through a spark gap, and this causes a diminu- 
tion in the arc voltage which permits the condenser to further 
discharge.- On account of inductance, the electricity keeps 
on flowing until the E. M. F. of the condenser is less than that 
of the arc. Ihen the condenser again begins to charge, and the 
cycle is completed. The result is a high-frequency current in 
the circuit shunted around the arc in Fig. 477, and continuous 
oscillations are imparted to the antenna circuit by means of the 
coupling. The choke coil prevents high-frequency currents from 



Choke Coil 




Resistance 



^y^'"" 




Fig. 477. — Direct-current Arc Transmitter. 

flowing in the generating circuit, and the resistance limits the 
current strength in the entire system, which is necessitated by 
the negative resistance coefficient of the arc. 

The principle upon which the vacuum tube acts to produce 
continuous electric oscillations is described in \ 387. 

383. Radio Frequency and Audio Frequency. — By adjust- 
ments of inductance and capacitance in the antenna and coupled 
circuits of transmission and receiving systems, it is possible to 
tune out other stations that may be transmitting at other 
radio frequencies than the one selected by a given transmission 
station. In a like manner, by using several spark frequencies, 
or the frequencies that ultimately reappear in the telephone 
receivers at the radio receiving station, different tones or notes 
will be heard in the telephone receivers, and these can be dis- 
tinguished from each other. The frequencies of these audible 
tones are called audio frequencies. 



598 LESSONS IN PRACTICAL ELECTRICITY 

Even when two messages are " coming in " at the same wave 
length or radio frequency but at sUghtly different spark or audio 
frequencies, it often is a simple matter, with practice, to dis- 
tinguish one from the other because of the difference in the 
pitch of the notes heard in the telephone receivers; In radio 
work during the recent war, there often were many stations 
transmitting simultaneously at the same wave length, so that 
in receiving a message from one of these transmitting stations 
it was necessary for the operator to concentrate on the dis- 
tinctive note of the station with which he was working. 

Attempts have been made to produce tuned telephone receivers 
which shall only respond to the audio frequencies for which they 
are adjusted. Such adjustments may consist in varying the 
tension or the mass, or both, of the vibrating elements of the 
telephone receivers. Should this become successful, it would 
become possible to have a considerable number of stations 
transmitting at Uke radio frequencies, but at different audio 
frequencies. 

384. Radio Receiving Sets. — All tuned radio receiving sets 
consist of an antenna circuit containing inductance, capacitance, 
and a certain amount of resistance. A second circuit contain- 
ing inductance, capacitance and resistance is coupled with the 
antenna circuit and in it are connected the telephone receivers 
which, as a unit, is the ultimate or last step in the chain of 
procedure from the transmission to the reception of radio sig- 
nals. The principal problem, then, in radio reception is to 
produce audible sounds in the telephone receivers when high- 
frequency or oscillating currents flow in the circuits of the 
receiving apparatus. 

The human ear cannot detect sounds having frequencies 
greater than 40,000 cycles per second, and very few persons can 
detect sounds at frequencies of more than 25,000 cycles per 
second. Even then, these sounds are very weak and require 
quiet and very close attention. The inertia of the diaphragm 
of a telephone receiver prevents it from responding readily to 
currents of more than 10,000 cycles, and the inductance of the 
electromagnet in a telephone receiver at these or higher fre- 
quencies prevents sufficient current flow to operate them satis- 
factorily even if the diaphragm did respond. Therefore, 



RADIO SIGNALING 599 

methods must be employed which either shall reduce the fre- 
quency of the current in a telephone receiver so that this 
exceedingly sensitive instrument shall function to the best 
advantage, or the character of the current must be changed. 

One way of accomplishing this result with incoming con- 
tinuous or undamped waves is to couple a very weak continu- 
ous-wave transmitting set with the receiving antenna circuit 
and adjust the frequency of this interfering apparatus slightly 
different from the frequency of the incoming waves. The 
effect is to produce heats, so familiar to musicians, which have a 
frequency equal to the difference between the above two fre- 
quencies, and are of sufficiently low frequency to satisfactorily 
operate a telephone receiver. If, for example, the frequency 
of the incoming oscillations is 200,000 cycles per second (wave 
length = 1500 meters) and the frequency of the local generat- 
ing set is adjusted to 202,000 cycles per second, then there 
would be 2000 beats per second and an audible note of 2000. 
cycles would be heard in the receiver. Between adjacent signals, 
the incoming wave either is absent, or is of a greatly different 
wave length (and frequency). Consequently; when there are no 
incoming waves, the resultant frequency of the receiving circuit 
is that of the local wave producer which is of radio frequency 
and, therefore, will not affect the telephone receiver. In the 
other case, the resultant frequency, which is equal to the differ- 
ence between the local and the incoming frequency, is purposely 
made so high as to be out of the audio frequency class, and, 
therefore, will not cause the telephone receivers to respond. 
This type of receiver is called a heterodyne receiver. 

Another method of receiving signals, transmitted by means of 
continuous waves, is to insert a circuit interrupter in the 
antenna or coupled circuit of the receiving set which shall 
cause the simulation of the " sound of a spark " in the tele- 
phone receivers. Such a circuit interrupter is called a tikker. 

The method employed for damped incoming waves is to 
rectify the feeble currents produced by the incoming high- 
frequency waves, so that the current shall flow only in one 
direction through the telephone receivers. By the aid of a 
small condenser, the equivalent of a unidirectional current is 
obtained for operaiting the telephone receivers during one wave 



600 



LESSONS IN PRACTICAL ELECTRICITY 



train. It should be borne in mind that there are several so- 
called '' wave trains " in each dot or dash signal. Conse- 
quently, for each incoming signal, the telephone receivers will 

respond to several 
pulsations of an 
audio frequency. 
This rectification of 
the oscillating an- 
tenna current is con- 
veniently accom- 
plished by means of 
crystal detectors, sl 
simple type of which 
is the silicon de- 
tector. This consists 
of a piece of " fused 
silicon," set into a 
cup of metal by 
means of some alloy 






Conc/ens0r 



Telephone 
^'Rzcefvers 



Fig. 478. — Crystal Detector Receiving Set. 



of low melting point, with a metal wire resting under shght 
pressure on the crystal. Such a detector has the property of 
unilateral conductivity and consequently the high-frequency cur- 
rents will flow through the 
detector in but one direc- 
tion. The simple circuit in 
Fig. 478 illustrates the prin- 
ciple. 

The receiving antenna in 
Fig. 478 contains both in- 
ductance and capacitance, 
and, therefore, will respond 
to incoming waves of a 
single frequency, and this 
frequency coincides with 
that at which the electricity in the receiving antenna naturally 
will oscillate. Assuming that such a wave train excites the 
receiving antenna circuit, the detector will permit the pulses of 
electricity to pass through it in one direction only. By insert- 
ing a small condenser in parallel with the telephone receiver 




'^ Telephones'' 

'^ Local Oscillah'ng Circuit 



Fig. 479. — Loose- coupled Receiving 
Set with Crystal Detector. 



RADIO SIGNALING 



601 



charges will be received upon it when the detector prevents 
the passage of electricity through the detector, the condenser 
discharging an instant later through the telephone receivers. 
This causes a pulsating flow of electricity through the telephone 
receivers at audio frequencies. 

Fig. 479 shows the connections of a form of loose-coupled 
receiving set. The arrows indicate that the condensers are 
adjustable, so as to vary the capacitance. 

385. Vacuum Tubes. — When the metallic filament of an 
incandescent lamp is heated to redness, the negatively-charged 
particles, or carriers of electricity, 
called electrons, in the filament 
are in such a state of agitation 
that they can be forced away 
from the filament and projected 
through the ether within the ex- 
hausted glass bulb, like bullets, 
provided there is a positively- 
charged member to which these 
electrons can go. This phenom- 
enon occurs best when all air is 
exhausted from the glass bulb. 

Fig. 480. illustrates a form of 
vacuum tube which may be used 
as a detector to rectify high- 
frequency alternating currents 
into currents flowing in one direction only, so that their 
presence may be detected by means of telephone receivers, 
relays, etc. The '' A " battery, usually a 4- volt storage bat- 
tery, heats the filament, and the " B " battery, with an E. M. F. 
of about 20 volts, is employed to force electrons from the 
heated filament, F, and to project them through the ether to 
the jplate, P. The positive side of the ^' B " battery is connected 
to the plate, and the negative side is connected to the filament. 
Then the negative side repels the negatively charged particles 
(electrons) from the filament, and they are attracted by the 
positively-charged plate. 

Referring to Fig. 480, with both switches Si and So closed, 
the filanient will be heated by cmTent flowing through it frorq 




Fig. 480. — Three-electrode 
Vacuum Tube. 

Comprises a filament, grid and plate 
within an evacuated glass bulb. 



602 LESSONS IN PRACTICAL ELECTRICITY 

the ^' A " battery, and electrons then will be repelled from the 
filament and attracted to the plate. If the polarity of the 
'' B " battery was reversed, no flow of electrons from filament 
to plate could occur because the electrons would be attracted 
to the filament and repelled from the plate. Also, if the switch 
Si was opened, there could be no flow^ of electrons under any cir- 
cumstances, because the filament then would be cold, and 
electrons cannot be emitted from a cold body of this character 
to any appreciable extent. 

When both switches in the circuit of Fig. 480 are closed, a 
stream of electrons will flow from the filament to the plate 
and will constitute an electric current, the strength of which 
will be the same in all parts of the circuit F-P-S2-B, because the 
electrons flow through the structures of the conductors consti- 
tuting the electric circuit. Therefore, if switch Si is rapidly 
opened and closed, a series of " clicks " will be heard in the 
telephone receivers or, if a relay is used, the armature of the 
relay will move to and fro. In what follows, the circuits will 
be assumed to be closed. 

That part of the vacuum tube thus far described is purely a 
local device which may be made as large or as small as prac- 
ticable. For instance, in a very large outfit, the telephone 
receivers might be replaced by the field coils of a direct-current 
motor, in which case, the function of the vacuum tube would 
be to control the speed of the motor. Therefore, the vacuum 
tube with its sources of energy may be considered as a power 
device, capable of delivering little or much energy to such 
devices as a telephone receiver, a relay, or a motor. While the 
amount of this energy may be controlled by the temperature 
of the filament (that is, by battery A) , it may be more con- 
veniently controlled by a grid, G in Fig. 480, located between 
the filament and plate. 

The effect of the grid is like that of a valve or a shutter 
which, opening or closing, controls the flow of electrons " through 
it " from the filament to the plate. The action of the grid may 
be compared with the action of a window shutter placed between 
a group of small boys armed with stones and, say, a tin plate 
at which the stones are hurled. When the shutter is opened, the 
stones go through and hit the tin plate^ but when the shutter is 



RADIO SIGNALING 



603 



closed no stones can go through it. The stones correspond to 
the electrons and the tin plate to the plate, P. 

The opening and shutting effect of the grid is accomplished 
by alternately giving it positive and negative charges. When 
the grid is positively charged, it tends to increase the flow of 
electrons from the filament to the plate. When the grid is 
negatively charged, it repels the electrons so that they will 
not go from the filament to the plate. When the grid is not 
charged at aU, there is nothing to prevent the electrons from 
going to the plate, and a current then flows through the plate 
circuit, which is that 
circuit including 
the telephone re- 
ceivers in Fig. 480. 
Therefore, when the 
grid is properly con- 
nected with a feeble 
source of alternat- 
ing current, there 
will alternately be 
positive and nega- 
tive E. M. F.'s be- 
tween the grid and 
the filament, so that 
the effect of rapidly 




Fig. 481. — Vacuum Tube Receiving Set. 



opening and closing the "shutter" above referred to will be 
obtained, and these feeble E. M. F.'s between the grid and the 
filament then control relatively great currents flowing in one 
direction in the plate circuit. 

386. The Vacuum Tube as a Detector and an Amplifier. — 
The action of the vacuum tube just described renders it suit- 
able for the detection of the feeble high-frequency currents in a 
receiving antenna. A simple receiving circuit is shown in 
Fig. 481. The tuned receiving circuit is connected to the input 
side of the tube, that is, to the filament and grid, and the 
telephone receivers are connected to the output side of the 
tube (plate circuit). Consequently, loud sounds may be heard 
in the telephone receivers when but a very small amount of 
energy is intercepted by the antenna. 



604 



LESSONS IN PRACTICAL ELECTRICITY 



Since the average human ear cannot detect sounds of fre- 
quencies above 25,000 C3^cles per second, all that can be heard 
in the telephone receivers are the ^' spark frequencies" of spark 
radio telegraph transmitting sets, since the vacuum tube in 




Fig. 482. — Vacuum Tube Amplifier and Detector. 

this case acts as a rectifier to produce a current in one direc- 
tion only in the telephone receivers. Obviously, the ear also 
can detect in the telephone receivers other variations in sounds 
caused by corresponding variations in the current strength pro- 
vided that they are within the audible range of frequencies like 
the human voice, for instance, which may be the reproduction 
of speech in a radio telephone set at a distant point. 

Since feeble E. M. F. variations in the grid circuit produce 

relatively great changes in the 
current strength in the plate 
circuit, the plate circuit may be 
coupled through a transformer 
to the grid circuit of a second 
vacuum tube to produce still 
greater changes in the current 
strength in the plate circuit of 
the second vacuum tube, and 
so on as far as may be desired. 
This principle of amplification 
is illustrated in Fig. 482. 
387. The Vacuum Tube as an Oscillation Generator or 
Oscillator. — By employing the general scheme of the amplifier 
on a single vacuum tube, as shown in Fig. 483, it may be used 




Fig. 483. — Connection Scheme 
of Oscillation Generator. 

The plate circuit is coupled with the grid 
circuit of the same tube in order to produce 
oscillations. 



RADIO SIGNALING 



605 



to generate oscillations. In this arrangement, the effect is 
much like that of a telephone '' howler " consisting of a tele- 
phone receiver placed near the telephone transmitter with 
which it is connected. The 
principle upon which the os- 
cillation generator operates 
sometimes is called the "feed 
back " principle, because the 
grid and plate circuits are 
made to react on each other 
much after the principle of 
the ''howler." 

By inductively coupling 
this arrangement wdth an 
antenna, a continuous-wave 
train may be transmitted 
which may be interrupted 
with a telegraph key to trans- 
mit telegraphic messages in 
code, or a telephone trans- 
mitter may be used to vary 
the amphtudes or strengths 
of the high-frequency oscil- 
lating currents so that artic- 
ulate speech may be trans- 
mitted to distant receiving 
stations. Fig. 484 illustrates 
the principle of superposing 
the voice waves on the high- 
frequency waves. This is 
accomphshed by means of 
another vacuum tube used as a modifier or modulator. The 
effect of the voice waves is to vary the amplitudes of the high- 
frequency carrier waves without altering the frequency. 

388. How the Waves Leave the Transmitting Antenna. — 
Consider a vertical aerial (lead-in wire only), as in Fig. 470, 
and assume that at a certain instant the top of the aerial is 
negatively charged, while the counterpoise, or ground, is posi- 
tively charged. A static strain is formed, as shown in Fig. 485, 




Fig. 484. — Modulating High-frequency 
Currents for Radio Telephony. 

Top: Audio frequency wave of "voice" 
current. 

Center: High-frequency or carrier wave. 

Bottom: Modulated wave formed by super- 
posing the voice current on the carrier wave. 



Transmifiing f^^^\ ^ \ ^ \ \ T 



606 LESSONS IN PRACTICAL ELECTRICITY 

by the E. M. F. impressed upon the antenna. When the an- 
tenna E. M. F. reverses, the counterpoise becomes negatively 
charged, the aerial becomes positively charged, and the wave 
immediately falls away from the aerial. The side of the wave 
next to the antenna is positively charged, and the positive 

charge at the bottom 
X of the antenna repels 

"^ ^ the wave into space. 
There is a repeUing ac- 
tion between adjacent 
wave sides; this is illus- 
.'x WXAX'^ '\ \ \\\ I J I V\ \ ' trated in Fig. 485, 
Vm^J^}AyM^^ wherein only the elec> 

+ "" '+ " trostatic field is repre- 

Fig. 485. — Propagation of Electromagnetic g^^ted for simplicity. 
Waves irom an Antenna. t , i • , i i ■ 

In this way the electro- 
magnetic waves, comprising the magnetic and electrostatic fields 
at right angles with each other, are launched from the trans- 
mitting antenna. 

389. Loop Reception. — As the electromagnetic waves strike 
a conducting body, such as a receiving aerial, E. M. F.'s are 
induced therein which rise and fall with the energy waves 
as they pass the aerial, and are of the same frequency as the 
energy waves. When two aerials are in the plane of a wave, 
so that the wave strikes one before the other, then, at a certain 
instant, the E. M. F.'s generated in each aerial will be in the 
same direction, but will have different magnitudes, so long as 
the aerials are spaced less than one-half wave length apart. 
If these aerials are connected together at their tops with a 
wire, and at their bottoms with another wire, so as to form a 
looy^ there will be two E. M. F.'s tending to neutralize each 
other, but since one has a greater magnitude than the other, 
the resultant E. M. F., equal to their difference, will produce a 
current in the loop. 

At any instant, the potentials of the waves in a certain locality 
may be represented by the sine curve, as in Fig. 486, in which 
the wave is assumed to move from left to right. AB and CD 
are two vertical wires connected at their tops and bottoms \:~; 
similar wires, so as to form a loop, pivoted about MN. A: a 



RADIO SIGNALING 



607 



given instant, when the loop is turned so as to be in the plane 
of the wave as the latter is passing across the surface of the earth, 
there is an E. M. F. induced in AB, the magnitude of which 
may be represented by Ax (the height of the wave at that point) 
and, say, in an upward direction. At the same instant, there 
is an E. M. F. induced in CD, the magnitude of which may 
be represented by Cz, and also in an upward direction. These 
two E. M. F.'s are opposing each other in the loop, but Cz is 





- 




N 








B 




D 




! 


1* 


\ Direch'on of Waves 


^ 


k 




\ Pis fane e 


^ M 













Fig. 486. — Principle of Loop Reception. 

greater than Ax by an amount equal to their difference, or yz; 
therefore, there will be present a resultant E. M. F., yz, which 
produces a current in the loop. 

390. Radio Direction Finder. — An important and interest- 
ing development during the World War is the radio direction 
finder with which it is possible to determine, with a high 
degree of accuracy, the direction from which radio waves are 
being received. Its most important application is in the navi- 
gation of vessels and airplanes. Bearings may be taken on 
distant known stations and, after applying certain corrections 
for the curvature of the earth, climatic conditions, etc., the 
location of the direction finder is determined by triangulation. 
The simplified apparatus consists of a vertically pivoted loop 
of wire, approximately five feet square with, say, twenty turns 



608 



LESSONS IN PRACTICAL ELECTRICITY 



of light wire, connected to some type of radio receiving apparatus 
containing an amplifier, as in Fig. 487. The loop, of course, 
contains inductance, and when shunted with a variable con- 
denser, forms a tuned or periodic circuit. To this combination 
is connected a receiving amplifier. No other aerial is necessary. 
Suppose that the loop, as previously described, is turned so 
that its plane is at right angles to the direction of the wave. 
Then, any point in the wave meets AB and CD of Fig. 486 at 
the same instant, and equal opposing E. M. F.'s are induced 
at all times. Their resultant is continually zero, and no cur- 
rent will flow in the loop. Therefore, the amount of energy 
received by the loop depends upon the angle which the loop 

makes with the wave, being a maxi- 
mum when the plane of the loop is 
parallel to the direction of the 
wave, and a minimum when the 
loop is in the right-angle position. 
Thus, with the loop connected to 
some detecting device, when the 
signal fades away as the loop is 
turned, it is known that the signal 
is coming from a direction which is 
at right angles to the plane of the loop. When the loop is in 
this position, a very slight change in the angle between the coil 
and the direction of wave propagation, makes a great difference 
in the amount of energy received and, therefore, in the strength 
of the signals. Consequently, the apparatus is very sensitive 
when in this position. However, it is quite insensitive when the 
plane of the loop is pointing towards the transmitting station, 
as a great change in the angle produces only a small change in 
the strength of the signals. 

In order to obtain increased sensitivity, a larger second, or 
auxiliary loop, is sometimes pivoted about the same axis with 
the main loop and fixed permanently at right angles to it as in 
Fig. 488. When the plane of the main loop is parallel to the" 
direction of the wave, it is receiving its maximum amount of 
energy, and the auxiliary loop is receiving the minimum amount 
of energy. Then, when the auxiliary loop is connected in series 
with the main loop, by means of a reversing switch, no differ- 



S 



To Receiving 
Amplifier 



Fig. 487. — Loop Antenna. 



RADIO SIGNALING 



609 



ence in the intensity of a signal should be heard in the telephone 
receivers when the reversing switch is thrown in either position. 
When the main loop is not in line with the radio wave, both 
loops- will receive energy, so that when the reversing switch is 
thrown in one direction, the energy received by the auxiliary 
loop will be added to that received by the main loop, thus pro- 
ducing a strong signal. When the reversing switch is thrown 
in the opposite direction, the resultant E. M. F. in the auxiliary 



Main Loop 



Auxiliary 
Loop 




Fig. 488. — Loop Antenna Employing Main and Auxiliary Loops for 
Increased Sensitiveness. 

loop opposes the resultant E. M. F. in the main loop, so that a 
weaker signal results. The loops can be placed easily and accu- 
rately so that no change in the intensity of the signals is noted 
when the reversing switch is thrown in either position. One 
of the loops then is in the plane of the wave. 

By first using the main loop alone, the transmitting station 
may be '' tuned in " and the approximate direction deter- 
mined, obtaining accuracy later by switching in the auxiliary 
loop. Since the energy received is very small, it is imperative 
that a strong multi-stage amplifier, like that shown in Fig. 482, 
be used. With such an apparatus as has been described, it is 
possible to obtain an accuracy of one degree when receiving 
several hundred miles from a powerful transmitting station. 



610 LESSONS IN PRACTICAL ELECTRICITY 



QUESTIONS 

1. What is the fundamental principle of radio signaling? ' 

2. What is a high-frequency current? ' 

3. What is the velocity of propagation of electromagnetic waves? 

4. How would you ascertain the wave length if the frequency of j 
oscillation is known? '■ 

5. What is an oscillating circuit? \ 

6. An antenna has a capacitance of 0.001 microfarad and an inductance I 
of 0.02 millihenry. What is its natural frequency and wave length? ; 

7. How are electromagnetic waves produced? : 

8. What is the difference between damped waves and continuous \ 
waves? ; 

9. Describe a few forms of counterpoise. ' 
10. What is meant by the directional effect of an antenna? \ 
IL How is the wave length of an antenna determined? • 

12. What is meant by damping and upon what factors does damping I 
depend? i 

13. What methods are employed for exciting the antenna circuit in j 
transmission systems? I, 

14. Describe how circuits are coupled. j 

15. What is the advantage of quenching the spark? ■ 

16. What is the principle of an arc transmission system? 

17. What is meant by radio frequency? and by audio frequency? \ 

18. On what general principles do radio receiving sets operate? . 

19. What is the function of a tikker? ■ 

20. What is the fundamental principle upon which a vacuum tube '■. 
operates? i 

21. Explain the action of a vacuum tube as an amplifier. 

22. How can a vacuum tube serve as an oscillation generator? 

23. Explain the principle of radio telephony? 

24. Describe the principle of loop reception. 

25. Explain how a radio direction finder is operated. • 



APPENDIX 



612 



APPENDIX 



Table XXII. Mensuration Rules 

f ^ (base X altitude). 



Area of triangle 



Area of parallelogram 
Area of trapezoid 
Circumference of circle 

Diameter of circle 

Area of circle 

Area of ellipse 
Area of regular polygon 
Lateral surface of cylinder 
Volume of cylinder 

Surface of sphere 

Volume of sphere 

Surface of pyramid or cone 
Volume of cone 



Vs(s - a) (s - b) (s - c), where a, h and c 

are the lengths of the sides and s = 

I (a + b + c). 
base X altitude. 

altitude x | sum of parallel sides, 
diameter x 3.1416. 

circumference x 0.3183. 

4 X area -h circumference. 

diameter squared x 0.7854. 

radius squared x 3.1416. 
product of diameters x 0.7854. 
^ (sum of sides x apothem) . 
circumference of base x altitude, 
area of base x altitude. 
/ diameter x circumference. 
\ 12.566X radius squared. 

diameter cubed x 0.5236. 

radius cubed x 4.189. 
^ (circumference of base x slant height). 
I (area of base x altitude) . 



■( 



Table XXIII. Conversion Table of Lengths 



To reduce 

Miles to kilometers 

" " yards 

" " meters 
Yards to meters 

" feet 
Feet to meters 

" " inches 
Inches to mils 

" " centimeters 
" " milhmeters 



Multiply by 

1.6093 
1760. 
1609.3 

0.91440 

3. 

0.30480 
12. 
1000. 

2.5400 
25.400 



To reduce 

Kilometers to miles 
" " meters 

Meters to miles 
" '* yards 
" " centimeters 
" feet 

Centimeters to milli- 
meters 

Centimeters to inches 

Millimeters to inches 



Multiply by 

0.62137 
1000. 

0.0006214 
1.0936 
100. 
3.2808 

10. 

0.39370 
0.039370 



Table XXIV. Conversion Table of Areas 

To reduce Multiply by To reduce 



Sq. miles to acres 640. 
Sq. yards to sq. meters 0.83613 
Sq. feet to sq. meters 0.09290 
Sq. inches to sq. centi- 
meters 6.4516 
Sq. inches to circular mils 1,273,238. 



Multiply by 



Sq. kilometers to sq. miles 0.3861 
Sq. meters to sq. yards 1.1960 

" " " sq. feet 10.764 

Sq. centimeters to sq. inches 0.15500 
" " " circular 

mils 197,861. 



APPENDIX 
Table XXV. Conversion Table of Volumes 



613 



To reduce 


Multiply by 


To reduce 


Multiply by 


Cu. yards to cu. meters 


0.76456 


Cu. meters to cu. yards 1.3080 


Cu. feet to cu. meters 


0.02832 


" " cu. feet 35.316 


" " " liters 


28.317 


Liters to cu. feet 


0.035317 


Cu. inches to cu. centi- 




Cu. centimeters to cu. 


meters 


16.387 


inches 


0.061027 


Cu. inches to hters 


0.01639 


Liters to cu. inches 


61.023 


Gallons to cu. inches 


231. 


" " cu. centi- 




" liters 


3.7854 


meters 


1000. 


Pounds of Avatsr to Hters 


0.4536 


Liters to gallons 


0.26417 


Table XXVI. Conversion Table of Weights 




To reduce 


Multii^ly by 


To reduce 


Multiply by 


Tons to kilograms 


907.18 


Kilograms to tons 


0.001102 


" " pounds 


2000. 


" " grams 


1000. 


Pounds to kilograms 


0.45359 


" pounds 


2.2046 


'' " ounces 


16. 


Grams to milHgrams 


1000. 


Ounces to grams 


28.349 


" " ounces 


0.03527 


'' " grains 


437.5 


" " grains 


15.432 


Grains to grams 


0.06480 


Grains to Troy ounces 480. 


Table XXVn. Conversion Tabl 


e of Force, Energy, Power, etc. 


To reduce 


Multiply by 


To reduce 


^Nluliply by 


Pounds to djmes 444,520. 


Dynes to pounds 


0.000002249 


Ft.-lbs. to kilogram- 




Kilogram-meters to 




meters 


0.13825 


ft.-lbs. 


7.233 


Ft.-lbs. to ergs 13,549,000. 


Ergs to ft.-lbs. 


0.0000000738 


" " joules 


1.3549 


Joules to ft.-lbs. 


0.7381 


" per second to 




H.P. to ft.-lbs. per 




horse power 


0.C01C2 


second 550. 


H.P. to watts 


746. 


Watts to H.P. 


0.001342 


B.T.U. to calories 


251.8 


Calories to B.T.U. 


0.003971 


Calories to joules 


4.1893 


Joules to calories 


0.2387 


Lbs. per sq. foot to kilo- 




Kilograms per sq. meter 


grams per sq. meter 


4.8824 


to lbs. per sq. foot 


0.2048 


Lbs. per sq. inch to grams 


Grams per sq. centimeter 


per sq. centimeter 


70.397 


to lbs. per sq. inch 


0.01422 


Miles per hour to feet pei 




Feet per sec. to 




sec. 


1.4667 


miles per hour 


0.68182 


Miles per hour to centi- 




Centimeters per sec. 




meters per sec. 


44.704 


to miles per hour 


0.02237 



614 



APPENDIX 



Table XXVIII. Comparative Table of Gages 

Giving the respective diameter and area of each number 





American Wire Gage 
(Brown & Sharpe) 


Birmingham Wire Gage 

(Stubs) 


Standard Wire Gage 
(British") 


Gage 

No. 


Diameter 


Area 


Diameter 


Area 


Diameter 


Area 




Inches 


Circular 
Mils 


Inches 


Circular 

Mils 


Inches 


Circular 
Mils 


7-0 
6-0 
5-0 
4-0 


0.4600 


211600. 


0.454 


206100. 


0.500 
0.464 
0.432 
0.400 


250000. 
215300. 
186600. 
160000. 


3-0 

2-0 



1 


0.4096 

0.3648 
0.3249 
0.2893 


167800. 

133100. 

105500. 

83690. 


0.425 
0.380 
0.340 
0.300 


180600. 

144400. 

115G00. 

90000. 


0.372 
0.348 
0.324 
0.300 


138400. 

121100. 

105000. 

90000. 


2 
3 

4 
5 


0.2576 
0.2294 
0.2043 
0.1819 


66370. 
52030. 
41740. 
33100. 


0.284 
0.259 
0.238 
0.220 


80630. 
67080. 
56610. 
48400. 


0.276 
0.252 
0.232 
0.212 


76180. 
63500. 
53820. 
44940. 


6 

7 
8 
9 


0.1620 
0.1443 
0.1285 
0.1144 


26250. 
20820. 
16510. 
13090. 


0.203 
0.180 
0.165 
0.148 


41210. 
32400. 
27230. 
21900. 


0.192 
0.176 
0.160 
0.144 


36860. 
30980. 
25600. 
20740. 


10 

; 11 

12 
13 


0.1019 
0.09074 
0.08081 
0.07196 


10380. 
8234. 
0530. 
5178. 


0.134 
0.120 
0.109 
0.0950 


17960. 

14400. 

11880. 

9025. 


0.128 
0.116 
0.104 
0.092 


16380. 
13460. 
10820. 
8464. 


14 
15 
16 
17 


0.06408 
0.05707 
0.05082 
0.04526 


4107. 
3257. 

2583. 
2048. 


0.0830 
0.0720 
0.0350 
0.0580 


6889. 
5184. 
4225. 
3364. 


0.080 
0.072 
0.064 
0.056 


6400. 
5184. 
4096. 
3136. 


18 
19 
20 
21 


0.04030 
0.03589 
0.03196 
0.02846 


1G24. 

1288. 
1022. 
810.1 


0.0490 
0.0-120 
0.0350 
0.0320 


2401. 
1764. 
1225. 
1024. 


0.048 
0.040 
0.036 
0.032 


2304. 
1600. 
1296. 
1024. 


22 

23 
24 
25 


0.02535 
0.02257 
0.02010 
0.01790 


642.4 
509.5 
404.0 
320.4 


0.0280 
0.0250 
0.0220 
0.0200 


784. 
625. 
484. 
400. 


0.028 

0.024 

• 0.022 

0.020 


784.0 
576.0 
484.0 
400.0 


26 
27 
28 
29 


0.01594 
0.01420 
0.01264 
0.01126 


254.1 
201.5 
159.8 
126.7 


0.0180 
0.0160 
0.0140 
0.0130 


324. 
256. 
198. 
169. 


0.018 
0.0164 
0.0148 
0.0136 


324.0 
269.0 
219.0 
185.0 


30 
31 
32 
33 


0.01003 
0.008928 
0.007950 
0.007080 


100.5 

79.70 
63.21 
50.13 


0.0120 
0.0100 
0.0090 
0.0080 


144. 
100. 

81. 

64. 


0.0124 
0.0116 
0.0108 
0.0100 


153.8 
134.6 
116.6 
100.0 


34 
35 
36 
37 


0.006305 
0.005615 
0.005000 
0.004453 


39.75 
31.52 
25.00 
19.83 


0.0070 
0.0050 
0.0040 


49. 
25. 
16. 


0.0092 
0.0084 
0.0076 
0.0068 


84.64 
70.56 
67.76 
46.24 


38 
39 
40 


0.003965 
0.003531 
0.003145 


15.72 
12.47 

9.888 


::: 




0.0060 
0.0052 
0.0048 


36.00 
27.04 
23.04 



INDEX 



[The figures refer to page numbers.]] 



Accumulators — see Storage Bat- 
tery 
Admittance of alternating-current 

circuit, 510. 
Aerial, definition of, 586. 
Aging of magnets, 7. 
Alternating current, average value 
of, 515. 
circuits, 494. 
effective value of, 512. 
frequency of, 497. 
generator — see Alternator, 
motor — see Motor, 
principles of, 494. 
representation of, 380. 
wave shape, 380. 
Alternations, 497. 

Alternator (s) armature — see Arm- 
atures, 
classification of, 535. 
construction of, 537. 
excitation of, 418. 
frequency of, 379. 
high-frequency, 589. 
inductor, 540. 
magnets, 381, 416. 
principle of, 338. 
rating of, 541. 
revolving-armature type, 535. 

-field type, 375, 537. 
self -exciting, 536. 
simple form of, 377. 
single-phase, 520. 
student's experimental, 377, 379. 
three-phase, 521. 
two-phase, 520. 
Amalgamation, 38. 



Ammeter, connecting, in circuit, 
258. 

D'Arsonval type, 252. 

dead-beat, 247, 340. 

dynamometer, 256. 

gravity type, 248. 

hot-wire, 251. 

inclined-coil, 249. 

shunts, 254. 

solenoidal, 248. 

Thomson, 249. 

types of, 247. 

Weston, 250, 252. 
Ampere, definition of, 85. 

-hour capacity of batteries, 172. 
definition of, 87. 

-meters — see Ammeters. 

-turn, definition of, 207. 
Amphfier, vacuum tube, 603. 
Angle of lag or lead, 518. 
Anode, definition of, 75. 
Antenna, definition of, 582, 

excitation, 589. 

loop, 606. 

types of, 586. 
Arc lamps, 464. 

radio transmitter, 596. 
Areas, table of, 612. 
Armature, alternating-current 
motor, 559. 

alternator, windings of, 537. 

closed-coil, 389, 395. 

coil assembly, 402. 
commutation of, 408. 

construction, 394. 

converter, 543. 

core, 394. 



615 



616 



INDEX 



Armature core, eddy currents in, 
396. 
hysteresis loss, 405. 
loss, 406. 
cross flux, 406. 
definition of, 23. 
direct-current, 389. 

example of, 405. 
drum, 393. 

E. M. F. induced in, 391. 
Gramme ring, 389. 
insulation, 401. 
laminations, 397. 
multi-coil, 385, 390. 

battery analogy of, 392. 
open-coil, 395. 
reaction, 406. 
resistance, 392. 
self-exciting alternator, 537. 
spider, 394, 
three-wire, 432. 
windings, 403. 
Audio and radio frequencies, 597. 
Automobile ignition systems, coils 
for, 348, 356. 
contact makers and dis- 
tributors for, 357. 
Auto-starter, 562. 

-transformers, 531. 
Ayrton shunt, 245. 

Balancer, 461. 

Ballistic galvanometer, 244. 

Barlow's wheel motor, 221. 

Battery — see Cell. 

Blasting, electric, 318. 

British thermal unit, definition of, 

309. 
Brush holders, 399. 
Brushes, carbon and copper, 400, 
position of, 409, 443. 

Calorie, definition of, 308. 
Candle power of lamps, 477. 
Capacitance — see Capacity. 
Capacity in alternating-current 
circuit, 505. 



Capacity of condenser, 503 

property of, 502. 

reactance, calculation of, 504. 

unit of, 503. 
Carrier waves, 605. 
Cathode, definition of, 75. 
Cautery, electric, 318. 
Cell(s), bichromate, 43. 

Bunsen, 45. 

carbon cylinder, 49. 

chemical action in, 33, 47. 

chemicals for, 52. 

classification of, 52. 

closed-circuit, 41. 

connected in multiple-series, 122. 
in opposition, 125. 
in parallel, 115. 
in series, 114. 
-multiple, 124. 

current from, 119. 

Daniell, 46. 

double-fluid, 41, 44. 

dry, 51. 

Edison-Lalande, 50, 

efficiency of, 157, 

electromotive force of, 35, 42. 

Fuller, 44. 

Gonda Leclanche, 48. 

gravity, 46. 

Grenet, 43. 

Grove, 45. 

internal resistance of, 68, 118. 

Leclanche, 48. 

local action in, 37. 

open-circuit, 41. 

parts of, 30. 

Partz acid gravity, 44. 

polarization of, 34. 
remedies for, 41. 

power from, 156. 

primary and secondary, 40. 

secondary, 161. 

size of, 112. 

Smee, 42. 

storage — see Storage Battery. 

voltaic, definition of, 29. 

Weston standard, 51. 



INDEX 



617 



Centigrade thermometer scale, 311. 
Chemical effect of current, 74, 82. 
Choke coil, 345. 
Circuit (s), admittance of, 5 ID. 

alternating- current, 494. 

breakers, 199. 

calculation of size of, 484, 

conductance of parallel, 510. 

coupled, 594. 

definition of electric, 129. 

distribution of potential in, 137. 

E. M. F. and current of, 133. 

for incandescent lamps, 480. 

impedance of, 505. 

magnetic — see Magnetic cir- 
cuits. 

power expended in, 150, 521, 

resistance of multiple-series, 106. 
of parallel, 103. 
of series, 102. 

resonant, 507. 

susceptance of parallel, 510. 

volts lost in, 135. 
Circular mil areas, 57. 
Clock rule for polarity, 194. 
Coils, spark and induction, 348. 
Commutating plane of dynamos, 
407.. 

-pole motors and generators, 412, 
452. 
Commutation, 384. 

improvements in, 410. 

process of, 408. 
Commutator, construction of, 398. 

function of, 382. 
Compass, gjTOScope, 12. 

mariner's magnetic, 10. 

pocket, 3. 
Compensated interpole motors, 413. 
Compensator, starting, 562. 
Condenser, construction of, 351. 

function of, 352. 

short-wave, 589. 

sjrnchronous, 575. 
Conductance, definition of, 105. 

method for parallel circuits, 106. 

of alternating-current circuit, 510. 



Conductive compensation of motors, 

568. 
Conductivity, definition of, 54. 

unilateral, 600. 
Conductors and insulators, 29, 54. 

calculating size of, 484. 

resistance of, calculating, 63. 
Consequent poles, 23. 
Controller for series motors, 459, 
Converters, rotary, 542, 
Cooking, electric, 319, 
Coohdge X-ray tube, 360. 
Copper, resistance of standard, 65. 
Coulomb, definition of, 86. 
Counter electromotive force of cell, 
126. 
of motor, 443. 
Counterpoise, definition of, 586, 
Coupled circuits, 594. 
Crystal detectors, 600. 
Current (s), active and reactive com- 
ponents of, 524. 

-carrying capacity of copper 
wires, 306. 

chemical generation of, 26. 

crossing, forces between, 226. 

direction of, 30. 

di\'ision in parallel circuits, 107. 

eddy, 338. 

effective value of, 512. 

effects of, 26, 72, 81. 

induced, 326. 

methods of obtaining, 332. 

kinds of, 72. 

lag or lead, 518. 

measurement of, 80, 247. 

parallel, forces between, 224. 

relations in transformers, 530. 

taken by motor, 445. 

transformer, 534. 

unit of, 85. 

used in commercial apparatus, 94. 
Cycle, significance of, 380, 497. 

D'Arsonval galvanometer, 242, 
Declination of compass, 8. 
Decrement of waves, 591. 



618 



INDEX 



A -connection, 533. 

Depolarizer, 41, 

Dielectric strength of air, 355. 

Dip needle, 8. 

Direct and inverse induced currents, 
333. 
-current generator — see Gener- 
ator, 
motor — see Motor, 
representation of, 385. 

Direction finder, radio, 607. 

Drop of voltage, 128. 

Dynamo — see Alternator, Gener- 
ator or Motor. 

Dynamometer ammeter, 256. 

Earth as a magnet, 7. 
Eddy currents, 338. 

in armature conductors, 402. 

cores, 396. 
loss due to, 396. 
Efficiency of battery, 157. 
generators, 436. 
lamps, 477. 
motors, 449, 490. 
storage battery, 178, 
transformers, 531. 
Electricity, effects and nature cf, 

26. 
Electrochemical series, 36. 
Electrodes of a cell, 30, 75. 
Electrodynamics, 222. 
Electrodynamometer, 256. 
Electrolysis, definition of, 26, 75. 
of copper sulphate, 75. 
lead acetate, 77. 
water, 74. 
zinc sulphate, 77. 
Electrolyte, definition of, 75. 

specific gravity of, 165. 
Electrolytic interrupter, 355. 
meter, Edison, 77. 
rectifier, 551. 
Electromagnet, 197. 
attractive force of, 215. 
forms of, 201. 
iron-clad, 151. 



Electromagnet, polarized, 204. 
Electromagnetic induction, 326. 
applications of, 348. 
waves, 579. 
Electromagnetism, 185. 
Electromotive force, counter, cf 
cell, 126. 
definition of, 32. 
direction of induced, 328. 
distribution of, 482. 
effective value of, 512. 
induced, 326. 

depends on change of mag- 
netic flux, 336. 
in armature, 391. 
methods of obtaining, 332. 
measurement of, 131, 259, 264. 
of primary cells, 35, 42, 98. 
self-induction, 500. 
short-circuited armature 

coils, 408. 
storage cells, 167, 177. 
thermo-couples, 323. 
relations in transformers, 529. 
Electron theory, 25. 
Electroplating, 77. 

current density in, 94. 
Electrostatic capacity, 503. 
Electrostatics, 26. 
Electrotyping, 78. 
End-cell switch, 138. 
Energy, conservation of, 151. 
definition of, 147. 
measurement of, 268. 
relation between forms of, 310. 
table of, 613. 
Equalizing bar of generator, 430. 
Equator, magnetic, 8, 20. 
Excitation of antenna, 589. 

generators, 416. 
Exciter, 419, 535. 

Fahrenheit thermometer scale, 311, 
Farad, definition of, 503. 
Faraday's disk dynamos, 339. 

law of induced E. M. F., 338. 
Flame arc lamps, 4G7. 



t 



INDEX 



619 



I 



Fluoroscope, 363. 
Flux density, 210. 
Foot-pound, definition of, 145. 
Force between magnet poles, 2, 17. 
parallel wires, 223. 

definition of, 144. 

exerted by electromagnet, 215. 

kinds of, 144. 

on wires in magnetic fields, 218. 

table of, 613. 
Frequency, audio and radio, 597. 

changer, 577. 

of alternating-current, 497. 

of alternator, 379, 498. 

oscillation, 584. 
Furnace, electric, 318. 
Fuses, 314. 

Galvanometer (s), astatic, 241. 

as voltmeters and ammeters, 231. 

ballistic, 244. 

classification of, 228. 

construction of students', 230. 

D'Arsonval, 242. 

dead-beat, 243, 340. 

differential, 241. 

mirror-type, 240. 

portable, 243. 

principle of, 228. 

sensibility of, 231. 

shunts, 232, 245. 

simple, 31, 229. 

tangent, 235. 

constants of, 239. 
measuring current with, 238. 

Thomson, 239. 
Gas-engine ignition, coils for, 348. 

hghting, electric, 348. 

voltameter, 81. 
Geissler vacuum tubes, 358. 
Generator (s), arc Hght, 426. 

armature — see Armatures. 

bipolar and multipolar, 374. 

capacity of, 434. 

classification of, 373, 416. 

compensating winding of, 411. 
' qompound-wound, 418, 427. 



Generator (s) 

constant-current, 416. 

-potential, 421. 
current regulation of, 426. 
definition of, 372. 
Dobrowolsky, 432. 
double-current, 393. 
efl5ciency of, 436. 
excitation of, 416. 
field, building up, 420. 

discharge of, 343. 

frames, 375, 411. 
heating of, 434. 
induced E. M. F. in, 376, 381 
interpole, 412. 
losses, 436. 

operating principle of, 445. 
parallel connection of, 423, 430. 
parts of, 372. 
principle of, 337, 376. 
rating of, 435. 
series, 416, 425. 

connection of, 424. 
shunt, 418. 
simple form of, 382. 
student's experimental, 377, 379. 
three-wire, 432. 
voltage regulation of, 422. 
Gramme ring armature, 389. 
Grill, electric, 319. 

Heat, calculation of, 308. 

electrical development of, 307. 
equivalent of, 308. 

equivalent of mechanical energy', 
151. 

units of, 308. 
Heating devices, electric, 318. 

effect of current, 72, 82. 

of conductors, 305. 

of generators, 434. 
Helix, polarity cf , 192. 
Henry, definition of, 343. 
Heterodyne receiver, 589. 
High-frequency alternator, 589. 
Horse power, definition of, 146. 
of steam engine, 147. 



620 



INDEX 



Hydrometer, 166. 
Hysteresis, meaning of, 340. 
loss in armature cores, 405. 

Impedance (s), calculation of, 501. 
definition of, 345. 
parallel connection of, 510. 
series connection of, 509. 
Incandescent lamps, 472. 
Inductance, definition of, 343. 
in alternating-currents circuit, 504. 
of solenoid, 344. 
property of, 499. 
unit of, 343. 
Induction, applications of, 348. 
coil(s), condenser for, 351. 
connections of, 350. 
construction of, 352. 
for ignition systems, 356. 
for X-ray machines, 362. 
in telephone sets, 365. 
principle of, 349. 
electromagnetic, 326. 
magnetic, 20, 210. 
motors, 554. 
self and mutual, 341. 
Inductive compensation of motors, 
568. 
line disturbances, 346. 
reactance, 345, 500. 
Inductor alternators, 540. 
Insulation of armatures, 401. 
resistance, measurement of, 230. 
temperature limits of, 434. 
test of machinery, 402. 
Insulators and conductors, 29, 54. 
Interpole motors and generators, 

412, 452. 
Interrupters for induction coils, 350, 

355. 
Inverse and direct induced currents, 

333. 
Ions, definition of, 75. 
Isogonic Hnes, 9. 

Joint impedance of circuits, 511. 
resistance of circuits, 104. 



Joule, definition of, 148. 

Joule's equivalent, 151. 

law of heating, 307. 

Keepers for magnets, 6. 
Kilo volt-ampere rating, 522. 
Kilowatt, definition of, 153. 
-hour, definition of, 154. 

Lag or lead of current, 518. 
Lamps, arc, 464. 

candle power of, 477. 

carbon filament, 472. 

distribution curves of, 480. 

efficiency of, 477. 

gas-filled, 475. 

incandescent, 472. 

life of, 477. 

mercury vapor, 470. 

rating of, 476. 

specific output of, 479. 

tungsten filament, 474. 

vacuum, 472. 

wiring calculations for, 484. 
Left-hand rule for force action on 

wires, 218. 
Lengths, table of, 612. 
Lenz's law of induced currents, 330. 
Lifting magnets, 203. 
Loading-back test of motors, 438, 

449. 
Local action in voltaic cell, 37. 
Lodestone, 1. 

Logarithmic decrement, 591. 
Logarithms, 592. 
Loop radio reception, 606. 
Lumen, definition of, 479. 

Magnet (s), artificial, 1. 
classification of, 1. 
definition of, 2. 
horseshoe, 6. 
laminated, 5. 
hfting, 203. 

making a permanent, 4. 
natural, 1. 



INDEX 



621 



Magnet (s), permanent, 2. 
application of, 6. 
poles, 2. 
Magnetic attraction and repulsion, 
2 
circuit (s), law of, 210. 

types of, 200. 
compass, 3. 
density, 210. 
dip, 8. 

effect of current, 73, 82. 
equator, 8. 
field, 18. 

around wires, direction of, 189. 
in generators, 407. 
intensity, 208. 
of bar magnets, 19. 

current-carrying wire, 186, 

190. 
horseshoe magnet, 21. 
parallel currents, 222. 
solenoid, 194, 198. 
force, 2, 17. 
hysteresis, 340. 
induction, 20, 210. 
leakage, 201, 216. 
lines of force, 18. 
map of United States, 9. 
meridian, 9. 
needle, 2. 

deflection of, by cm-rent, 187. 
polarity of circular current, 191. 

of iron ring, 200. 
saturation, 17. 
screens, 22. 
substances, 3. 
Magnetism, molecular theory of, 15, 
nature of, 15. 
of the earth, 7. 
residual, 17. 
Magnetite arc lamp, 468. 
Magnetization by electric currents, 
5, 196. 
by stroking with magnets, 4, 
curves, 214. 
Magneto alternator, 381, 416. 
telephone, 366, 382. ^ 



Magnetomotive force, calculation 
of, 208. 
definition of, 207. 
Mariner's compass, 10. 
Mass and weight, 145. 
Mazda lamps, 474. 
Mechanical equivalent of heat, 151, 
Medical coil, design of, 353. 
*' Megger" testing set, 301. 
Megohm, definition of, 55. 
Mensuration rules, 612. 
Mercury arc rectifier, 545. 

vapor lamps, 470. 
Microfarad, definition of, 503. 
Microhm, definition of, 55. 
Milliammeters, 248. 
Millivoltmeters, 254. 
Molecular theory of magnetism, 

15. 
Motor(s), alternating-current, clas- 
sification of, 554. 
armature — see Armatures, 
compound-wound, 459. 
counter E. M. F. of, 443. 
current taken by, 445. 
definition of, 372. 
direct-current, classification of, 

440. 
direction of rotation of, 387, 442. 
efficiency of, 449, 490. 
elementary forms of, 220. 
-generator sets, 461, 576. 
induction, polyphase, 554. 
rotors for, 559. 
single-phase, 564. 
speed control of, 561. 
squirrel-cage, 559. 
starting, 561. 

synchronous speed of, 555. 
theory of, 554. 
wound rotor, 560. 
interpole, 412, 452. 
output, testing, 448. 
power exerted by, 448. 
principle of, 386. 
repulsion, 566. 
-induction, 569. 



622 



INDEX 



Motor (s), series, characteristic 
curves of, 457, 
for cranes, 455. 
railway, 458. 
single-phase, 567. 
shunt, adjustable-speed, 412, 
452. 
characteristic curves of, 455. 
principle of, 445. 
speed control of, 452. 
regulation of, 454. 
starting of, 450. 
single-phase commutator, 566. 

induction, 564. 
synchronous, 572. 
self-starting, 574. 
starting of, 575. 
torque of, 448. 
wiring calculations, 4S9. 
Multiple circuits, 102, 133. 
-series connection, 106. 
of cells, 122. 
Multipliers for voltmeters, 262. 
Multiplying power of a shunt, 233, 

256. 
Mutual induction, definition of, 341. 

Navigation, earth's magnetism 

used in, 8. 
Non-inductive windings, 70, 345. 

Ohm, definition of, 54. 
Ohmmeters, 298. 

Ohm's Law applied to battery cir- 
cuit, 108. 
for alternating-current circuits, 

507. 
for direct-current circuits, 99. 
Oscillation constant, 584. 
electric, 582. 
transformer, 593. 
Oscillator, vacuum tube, 605. 

Parallax, errors due to, 254. 
Parallel circuits, 103, 133. 
connection of cells, 115. 
of impedances, 510. 



Percolators, electric, 319. 
PermeabiUty, definition of, 211. 

table for iron and steel, 212. 
Phase, significance of, 518, 
Polarity indicator, 79. 

of a magnet, 2. 

of a solenoid, 192. 
Polarization of cells, 34, 

remedies for, 41. 
Polarized electromagnets, 204. 

relays, 205. 
Pole, consequent, 23. 

of a magnet, 2. 

pieces, 23. 
Polyphase motors — sse Motors. 

system, 521. 
Potential, definition of, 32. 

difference, measurement of, 259. 

distribution in circuits, 137. 
Potentiometer, 264. 
Power, apparent, 522. 

calculation of, 150, 521. 

definition of, 146. 

electrical, 149. 

exerted by a motor, 448. 

factor, 522. 

in alternating-current circuits, 
513. 

in direct-current circuits, 150. 

measurement of, 268, 522. 

table of, 613. 

transmission, 530. 

units of, 146, 150, 153. 
Pressure — see Electromotive 

Force. 
Prony brake, 449, 
Pyrometry, 321. 

Quantity of electricity, unit of, 86. 
Quenched spark gap, 595, 

Radiation of waves, 579. 

resistance, 593. 
Radio and audio frequencies, 597. 

detectors, 600. 

direction finders, 607. 

receivers, 598. 



INDEX 



623 



Radio telegraphy and telephony, 
579. 
transmitters, 589. 
Radiographs, 359. 
Railway motors, 458. 
Ratio of conversion, 544. 
transformation, 529. 
Reactance, capacity, 504. 

inductive, calculation of, 500. 

definition of, 345. 
voltage in armatures, 408. 
Rectifier, electrolytic, 551. 
mercury arc, 545. 
tungar, 549. 
types of, 545. 
vibrating, 547. 
Reflectors and shades, 480. 
Relay, telegraph, 205. 
Reluctance, calculation of, 213. 
definition of, 210. 
of magnetic circuits, 211. 
Repulsion motors, 566. 
Resistance (s), commercial and lab- 
oratory, 68. 
definition of, 54. 
effect of temperature upon, 61, 

312. 
in multiple-series, 106 
parallel, 103. 
series, 102. 
laws of, 60. 

measurement by comparative 
drop method, 281. 
direct deflection method, 283. 
"megger," 301. 
ohmmeter, 298. 
sHde-wire bridge, 290. 
substitution method, 281. 
voltmeter-ammeter method, 

280. 
voltmeter method, 282. 
wheatstone bridge, 284, 293. 
of armature, 392. 
cells, 68, 118. 
conductors, 60. 

calculation of, 63. 
connections, 69. 



Resistance (s) , radiation, 593 . 

relative, 65. 

specific, 63, 65. 

standards of, 279. 

temperature coefficient of, 312. 

unit of, 54. 
Resistivity, 63, 65. 
Resonance of circuits, 507. 
Retentivity, 17. 
Rheostats, field-regulating, 421, 453. 

laboratory, 70. 

starting, 69, 451. 
Right-hand rule for direction of 
magnetic field, 189. 
of induced E. M. F., 328. 
Ringer, telephone, 205. 
Roentgen rays, 359. 
Roget's jumping spiral, 225. 
Rotary converters, 542. 

Self-induction, definition of, 341. 
illustrations of, 342. 
neutralizing effects of, 345. 
Series circuits, 102. 

connection of cells, 114. 
of impedances, 509. 

generators, 416, 425. 

motor, single-phase, 567. 
direct-current, 442. 

-multiple connection of cells, 124. 
Shunt generators, 418, 421. 

motors, 442. 
Shunts for ammeters, 254. 

galvanometers, 232, 245. 
Sine curve, plotting a, 495. 
Sinusoidal wave shape, 381. 
SHde-wire bridge, 290. 
SUp of induction motors, 559. 
Solenoid, attractive force of, 198. 

inductance of, 344. 

magnetic field of, 194. 

polarity of, 192. 
Sounder, telegraph, 202. 
Spark coils, 348. 

gaps, 590, 595. 

radio sets, 590. 
Sparking at dynamo brushes, 408. 



624 



INDEX 



Sparking, causes of, 413, 568. 

distances in air, 355. 
Specific gravity of electrolytes, 165. 
output of lamps, 479. 
resistance, 63, 65. 
Speed control and regulation of 
shunt motors, 452. 
of induction motors, 561. 
Square mil areas, 58. 
Starting box, 69, 451, 564. 

compensator, 562. 
Static electricity, nature of, 26. 
Steam engine, horse power of, 147. 
Storage battery, capacity of, 172. 
charge and discharge, 163, 174. 
chemical action in, 163. 
constant-potential charging of, 

182. 
definition of, 161. 
Edison, 175. 

chemical action in, 177. 
electrolyte of, 176. 
voltage of, 177. 
efficiency of, 178. 
Exide form, 171. 
Faure type, 168. 
Gould plate, 169. 
Iron-clad form, 172. 
lead-acid, 163. 
care of, 174. 
chemical action in, 163. 
electrolyte of, 165. 
types of plates, 168. 
voltage of, 167. 
Manchester plate, 169. 
methods of charging, 179. 
nickel-alkali, 175. 
normal discharge rate, 172. 
Plant e type, 162, 168. 
Tudor plate, 169. 
uses of, 182. 
Stove, electric, 319. 
Susceptance of alternating-current 

circuit, 510. 
Switchboards, 369, 483. 
Switches, end-cell, 138. 
Synchronizer or synchroscope, 575. 



Synchronous condenser, 575. 
converter, 542 
motors, 572. 
speed, 555. 

Tangent galvanometer, 235. 

of an angle, 236. 
Telegraph relay, 205. 

sounder, 202. 
Telephone hook switch, 366. 

induction coils, 365. 

line transposition, 346. 

magneto, 366. 

receiver, 364. 

ringer, 205. 

subscribers' sets, 367. 

switchboards, 369. 

systems, 367. 

transmitter, 364. 
Temperature coefficient of resist- 
ance, 312. 

measurement by resistance change, 
321. 

of dynamos, measuring, 435. 
Thermo-couple, 322. 

-electric pyrometer, 322. 
Thermometer scales, 311. 
Thermostats, 320. 
Thomson galvanometer, 239. 

inclined-coil, ammeter, 249. 

watt-hour meter, 270. 
Three-wire generators, 432. 
system, balancer for, 461. 
purpose of, 487. 
Torque, significance of, 243, 448. 
Traction, electric, 459. 
Transformers, auto-, 531. 

connections of, 534. 

coohng of, 528. 

current, 534. 

current and voltage relations of, 
529. 

efficiency of, 531. 

for X-ray machines, 361 

function of, 527. 

losses in, 533. 

oscillation, 593. 



INDEX 



625 



Transformers, ratio of, 529. 

regulation of, 531. 

types of, 527. 

used in auto-starters, 562. 
in welding machines, 317. 
Tungar rectifier, 549. 

Vacuum tube amplifier, 603. 
Geissler, 358. 
oscillator, 604. 
receiving set, 603. 
three-electrode, 601. 
Vapor lamps, 470. 
Voltage — see also Electromotive 
Force, 
drop, 128. 

regulation of generator, 422. 
of transformers, 531. 
Voltaic cell — see Cell. 
Voltameter calculations, 89. 
construction of, 90. 
definition of, 75. 
gas, 81. 

measurements with, 91. 
weight, 88. 
Voltmeters, connecting, in circuit, 
263. 
permanent magnet for, 7. 
principle of, 259. 
Weston, 261. 
Volumes, table of, 613. 

Watt, definition of, 150. 
-hour, definition of, 153. 
meter, circuits of, 273, 275. 
damping by eddy currents, 

340. 
magnet for, 7 
Sangamo, 274. 
Thomson, 270. 
Wattmeter, connecting, in circuit, 
269. 
construction of, 268. 



Wattmeter, Weston portable, 270. 
Wave-length, calculation of, 584. 
definition of, 581. 
optimum, 588. 
shape, alternating-current, 380. 
Waves, carrier, 605. 

damped and continuous, 585. 
propagation of, 605. 
Wehnelt interrupter, 355. 
Weights, table of, 613. 
Welding machine, electric, 316. 
Wheatstone bridge, decade dial 
form, 297. 
plug form, 295. 
in pyrometry, 322. 
lamp analogy of, 288. 
lozenge form, 284. 
operation of, 288. 
"Post-Office" form, 292. 
Queen- Acme form, 293. 
theory of, 285. 
Wire(s), calculating resistance of, 
64. 
current-carrjdng capacity of, 306. 
gage, 66. 

table of, 614. 
loss on, 484. 

measure, the circular mil, 57. 
table, copper, 67. 
transposition of, 346. 
voltage drop in, 139, 484. 
weights of, 65. 
Wiring, calculation of, 484, 489. 

installation of, 490. 
Work, calculation of, 148. 
definition of, 145. 
electrical, 148. 
units of, 145, 148, 153. 

X-ray machines, 362. 
X-rays, 359. 

Y-connection, 533. 



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